What are economic exchanges? The received view has it that exchanges are mutual transfers of goods motivated by inverse valuations thereof. As a corollary, the standard approach treats exchanges of services as a subspecies of exchanges of goods. We raise two objections against this standard approach. First, it is incomplete, as it fails to take into account, among other things, the offers and acceptances that lie at the core of even the simplest cases of exchanges. Second, it ultimately fails to generalize to exchanges of services, in which neither inverse preferences nor mutual transfers hold true. We propose an alternative definition of exchanges, which treats exchanges of goods as a special case of exchanges of services and which builds in offers and acceptances. According to this theory: (i) The valuations motivating exchanges are propositional and convergent rather than objectual and inverse; (ii) All exchanges of goods involve exchanges of services/actions, but not the reverse; (iii) Offers and acceptances, together with the contractual obligations and claims they bring about, lie at the heart of all cases of exchange.
“what is really exchanged, whether a commodity
intervene or not, are mutual services.”
A. L. Perry, Elements of Political Economy (1878, p. 86).
Economic exchanges are fundamental economic phenomena, so much so that economics, standardly defined as the study of the allocation of scarce resources (Menger 1976, p. 77–113; Robbins 1984, p. 12–15), is sometimes alternatively defined as the science of exchanges or “cattalactics” (Bastiat 1996, p. 59; Buchanan 1964, p. 213–222; Buchanan 2001, p. 27–32 ). Given the centrality of the concept of exchange in economics, it is surprising how little attention has been paid to the nature of exchanges. Economists have extensively studied the conditions in which exchanges occur and the role that exchanges play in the determination of prices and equilibria. In collaboration with philosophers, they have assessed various normative issues pertaining to exchanges, such as the positive and negative externalities they bring forth, the irrationality of some exchanges, or the potential ethical issues raised by certain species or conditions of exchanges, such as asymmetries in bargaining power.
But historical and contemporary economics literature rarely ever addresses what exchanges are. The main exceptions are the early Austrian marginalists, who, insightfully if rather briskly, explicitly stated the account of exchanges that economists appear to implicitly rely on. In most textbooks, however, the nature of exchanges is just assumed to be intuitively clear, and accounts of exchange-value, prices, efficiency, partial equibrium, etc.  are then developed on the basis of a pre-theoretical grasp of exchanges.
Our goal in this paper is to provide a precise answer to the question: what are economic exchanges? We want to highlight that, although we shall argue that one of the most basic concepts of economics, exchange, has not been properly defined so far, we do not contend nor think that this has undermined economic theorizing. The pre-theoretical and tacit understanding of exchanges has proven sufficient for economic purposes. Why then bother about the nature of exchanges, if an explicit and detailed understanding of them is supererogatory from the economic standpoint? Here are two answers.
First, we take this question to be of intrinsic interest, irrespective of the consequences it may have for economic theorizing. Exchanges are pervasive social phenomena, and scientists interested in the social world should be eager to get a proper understanding of them. In other words, rather than using exchanges as explanantia used to shed light on other phenomena (such as, typically, exchange value, prices), taking exchanges as our explananda is, we submit, an epistemically valuable inquiry.
Second, as we shall suggest, although the standard conception of exchanges may have been good enough so far, it now stands in tension with two well-established directions in recent economic research. The first is, under the influence of rational choice and game theory, the move away from an early focus on goods to a new focus on actions. The standard conception of exchanges, modeled on exchanges of goods, has thus become at odds with contemporary game-theoretic approaches to microeconomics whose starting points are preferences ranging over actions rather than commodities. Second, a growing amount of research lies at the intersection of economics and law. The standard conception of exchanges, not taking into account the normative aspects of exchanges, fails to draw any clear link between exchanges and law. By contrast, the action-theory of exchange we shall advocate is more in tune with such recent developments in economics. While still being able to account for exchanges of goods, it views exchanges of actions as the most basic phenomena, in accordance with game theory. Furthermore, by putting emphasis on offers, understood as conditional promises, it provides a straightforward way to connect exchanges with contractual obligations.
In Section 2 we introduce what we take to be the standard theory of exchanges, which we retrieve from various tacit and explicit assumptions widely made across the economic literature. Section 3 argues that the standard theory is incomplete as its stands, and that it cannot be easily completed. Section 4 argues that the standard theory also fails to give necessary conditions for exchanges: in particular, it fails to account for exchanges of services. In Section 5 we introduce the theory of exchanges we advocate, which we call the action theory. Section 6 explains how the action theory, modeled on exchange of services, accounts for exchanges of goods. Section 7 compares the action theory of exchanges to the standard theory, and concludes that the action theory fares better in all respects.
2 The Standard Theory of Exchanges
2.1 The Standard Theory introduced
For simplicity, we shall here focus on exchanges between two agents, involving only two entities exchanged. For example, what is it for Julie to sell her bike to Paul?
One intuitive answer (which, although rarely explicitly spelled out, is widely shared among economists, as we shall argue) goes as follows: for Julie to sell her bike to Paul, it has to be the case that (i) Julie prefers Paul’s money to her bike, (ii) Paul prefers Julie’s bike to his money, and that, in virtue of these inverse preferences, (iii) Julie voluntarily transfers her bike to Paul and (iv) Paul voluntarily transfers his money to her. More generally, exchanges consist in mutual transfers of goods, motivated by the exchangers’ inverse valuations of these goods – where by “inverse valuations” we simply mean that each exchanger values the good of the other more than his own. (We shall here assume throughout that money is a kind of good).
Standard theory of voluntary economic exchange (STE): if A and B exchange their goods x and y, then:
A prefers y to x
B prefers x to y
A voluntarily transfers x to B
B voluntarily transfers y to A
(2.1.) partly because of (1.1); (2.2) partly because of (1.2).
The “because” in the last condition is the because of subjective reason: each exchanger’s preference motivates him to transfer his good. Note that the STE only spells out some necessary conditions for exchanges. It is not intended to give the complete story about them.
The STE is meant to be widely encompassing, being true of barters (“direct exchanges”) as well as monetary exchanges (“indirect exchanges”). Hence the preferences at stake might be final or instrumental. Presumably, Julie’s preference for money is instrumental, that is, she wants money because of the purchasing power it confers; Paul’s preference for the bike is, typically, not instrumental in this way: Paul does not value the bike as a means of exchange.
Most importantly, the notion of “good” (or “commodity”) employed in the STE is meant to be very generic: goods include immaterial goods (alternatively called intangible goods) as well as tangible goods. This distinction between tangible and intangible goods is key to the STE’s handling of exchanges of services. To apply the STE to exchanges of services, one just needs to identify services as a sub-species of intangible goods. Therefore, a fundamental presupposition of the STE is that goods and services belong to the same ontological category, namely the category of objects (an assumption we shall challenge below).
That exchangeables are material or immaterial goods (the latter of which includes services) is arguably the overarching feature of the STE. For once it is admitted that what is exchanged are the goods of the exchangers, the idea that exchanges essentially involve transfers of good becomes almost irresistible: how could an exchange take place without goods changing hands? And why would such a swapping of goods ever take place if the exchangers were not to value the exchanged goods in inverse fashion? How else are we to account for the motivation to exchange goods if not by these inverse valuations?
This is precisely how the appeal to inverse preferences is justified. The idea is simply that exchanges would not take place in their absence. If potential exchangers were to value goods in exactly the same way, they would never bother exchanging. What is the point of exchanging a one-dollar coin against another, or a 1982 Chateaux Margaux against an exactly similar one? Exchangers are willing to exchange because each exchanger values, ex ante, the other’s good(s) more than his own. Each exchanger thus expects to be better off after the exchange. Such ex ante valuations might prove wrong. Exchangers might regret the exchange: they can be disappointed by the good they received, or the good they have given up might retrospectively appear more valuable to them. Still, agents engage in exchanges because they expect, correctly or not, that their satisfaction will increase as a result.
Although, following the standard contemporary microeconomics, we have equated the states motivating mutual transfers with preferences, the core idea need not be expressed in terms of preferences. The STE might be spelled out in terms of “A wants/desires/needs/values/likes… x more than A wants/desires/needs/values/likes… y” rather than “A prefers x to y”. A preference is a single attitude with a comparative content: Prefers(x,y). On the other hand, Liking more and its cognates are pairs of attitudes, each with a typically non-comparative content: Likes(x) more than Likes(y). One might think that preferences are internal relations supervening on monadic attitudes of different degrees, or deny it (Mulligan 2015). The STE is not committed to any of these views. Since the following discussion of the STE and its rivals is meant to hold true whether these views are framed in terms of preferences or of liking more, we shall henceforth ignore this distinction, and use the terms “preferring”, “liking more”, “valuing more” interchangeably. In the present context, the only three essential points about these comparative attitudes are:
that such attitudes be objectual rather than propositional. They target goods (x’s and y’s) rather than propositions or states of affairs (p’s and q’s)
that some comparison takes place between these goods (either within the content of such objectual attitudes –preferences; or between such attitudes – liking more);
that the valuations of the two exchangers be the inverse of each other, that is, that the good that one exchanger values more, or prefers, is the one that the other exchanger values less, or disprefers.
Thanks to the introduction of inverse preferences, upholders of the STE are in a position to reject two simplistic views of exchanges, which have been thought to form a dilemma:
Either exchanges are “exchanges of equivalent”, in the sense that the goods exchanged are of equal values (Aristotle, Nic. Ethic, V, 5, 1133a, 24) (Aristotle, 1954), and nobody gains from exchanging.
Or the goods exchanged are of unequal values, and the profit of one exchanger is the loss of the other (a view often attributed to Montaigne, albeit controversially so ).
One reason why both horns of the dilemma are unattractive is that, if exchanges are necessarily either pointless or detrimental to one exchanger, it becomes unclear why exchanges are so ubiquitous. Once inverse valuations are taken into account, the dilemma turns out to be a false one. Because exchangers value goods in reverse ways, both gain from exchanging. No contradiction is involved since the values motivating exchanges are subjective: in Julie’s eyes, Paul’s money has more value than her bike; in Paul’s eyes, Julie’s bike is more valuable than his money. (To anticipate: we shall agree that the dilemma above needs to be escaped, and we shall also agree that goods exchanges are in the end motivated by inverse preferences. But we shall argue in Section 7 that the fundamental sense in which all exchanges – of goods as well as of services – are mutually beneficial is that they satisfy convergent rather than inverse preferences of the exchangers.)
The STE is therefore committed to a subjectivist understanding of the values motivating exchanges (which is not to exclude objective values, but just to claim that these are not the ones motivating exchanges). What prompts exchanges are not the objective values of the goods that are exchanged (for instance, the quantity of labor they incorporate, or their objective esthetic worth) but rather the exchanger’s subjective valuations of the goods at stake. More precisely, it is the subjective value of an additional unit of that good to the subject, given what he already possesses – the marginal utility of that good – that lies behind the subject’s preferences. Thus the STE is naturally combined with a marginalist approach to economic value.
Additionally, the STE as it stands is compatible with (but does not entail) methodological individualism, the view that only individuals think and act. The valuations at stake in an exchange are the individual mental states of each exchanger. Likewise, the two transfers are two individual actions. No “we”, no sense of “common interest”, no “collective intentionality” or “joint action”, is required for exchanges to take place.
2.2 How Standard is the Standard Theory?
Few economists, we take it, would readily recognize in the STE the standard economic view of exchanges. A first reason for this may simply be terminological. Instead of “goods” one often finds “commodities”, “resources” or even “values”; instead of “transferring” one often finds “ceding”, “giving up”, “delivering”, “selling”, etc.; instead of “S prefers x to y” one often finds “S values x more than y”, “x has a higher (marginal, expected) utility for S than y”, “x is better for S than y”, “S is willing to give up x for y”, etc. 
But the main reason why the STE may not look like a standard piece of economic theorizing is that it is in fact virtually never explicitly spelled out in the economics literature. The main exceptions are Austrian economists, who, certainly because they share philosophers’ taste for a priori truths, definitions and metaphysical inquiries (Smith 1990), have paid explicit attention to the nature of exchanges. To our knowledge the most detailed version of the STE is the one advanced by Menger in his Principles of Economics:
The most general form of the relationship responsible for human trade is therefore as follows; an economizing individual A, has a certain quantity of a good at his disposal which has a smaller value to him than a given quantity of another good in the possession of another economizing individual, B, who estimate the values of the same quantities of goods in reverse fashion, the given quantity of the second good having a smaller value to him than the given quantity of the first good which is at the disposal of A. […] If, in addition, the two economizing individuals (a) recognize the situation and (b) have the power actually to perform the transfer of the goods, a relationship exists that makes it possible for them, by a mere agreement, to provide better or more completely, for the satisfaction of their needs than would be the case if the relashionship were not exploited. (Menger 1976, p. 179–180).
But, Austrian economists aside, economists generally take the phenomenon of exchange to be obvious enough to constitute an unanalysed explanans. In doing so, they nevertheless make a certain number of tacit assumptions about exchanges. The STE, we contend, captures these assumptions.
As we saw, the three core assumptions of the STE are (i) that exchangeables are goods (material or immaterial); (ii) that exchanges involve mutual transfers of these goods; and (iii) that exchanges are motivated by inverse valuations of these goods. We shall now argue that, terminological variations aside, these three assumptions are standardly admitted across economic textbooks.
Consider first the view that exchangeables are goods (or bundles, baskets thereof). This assumption is shared not only by Austrians, but by nearly all early neoclassical economists. Walras (1874, p. 70) refers to “commodities” (“marchandises”). He insists that exchangeables are commodities, and that these belong to the category of things. Following him, microeconomics assumes that trade bears on goods, commodities, or bundles thereof. One clear symptom of this is that the variables of economic formalizations are individual variables (x, y, z…), not propositional ones (p, q, r…). The preferences appealed to in economic theorizing are objectual preferences (preferring x to y) rather than propositional ones (x prefers to F rather than to G; x prefers that p rather than that q). Indifference curves, for instance, are held to represent the possible combinations of two (bundles of) goods between which consumers are indifferent.
Why such a focus on goods? Why does economics tend to give priority to goods over services by subsuming the later under the former? One chief reason for this, advanced by Hill (1976, 1999), is that economics is often conceived as studying the allocation of scarce resources and relatedly, as bearing on wealth, usually conceived in terms of possession of goods. Under this conception of economics, the only way for services to be included in its field of inquiry is for them to make a difference in the wealth of individuals (or nations). For this, services need to be seen as allocatable resources, that is, as goods. If, on the other hand, being rendered a service does not consist in being allocated a good, then it does not necessarily make one richer, which led Smith to call service rendering “unproductive labor” (Smith 1904, Book II, Ch. III). In other words, if wealth and allocation of scarce resources are the focus of economics, then either services have to be equated with allocatable objects – i.e. goods – or they are not of immediate interest to economics. The first option has been widely accepted, as amply documented by Hill (1999), and as a consequence exchanges of services are seen as sub-cases of exchanges of goods.
Is this objectual approach to exchanges still at play in contemporary microeconomics, however? This may appear doubtful at first. Microeconomics, as presented in today’s advanced textbooks (e.g. Kreps 1990; Mas-Colell et al. 1995), is an application of expected utility theory and game theory, for which preferences bear not on commodities, but on actions. However, oddly enough, when thinking and writing about exchanges, contemporary microeconomics routinely relapses into its old objectual mindset.
Thus, when rational choice theory is put to use to understand markets, economics textbooks typically revert back to the traditional assumption that commodities are “the objects of choice for the consumer” (Mas-Colell et al. 1995 p. 17; see also Kreps 1990, p. 18–19, Arnold 2016, p. 26). In one of the few works explicitly aiming at providing a game-theoretic approach to economic exchanges, Hardin (1982, p. 251–252) continues to waver rather freely between goods- and action-based approaches to exchangeables. The survival of this objectual mindset is also apparent in the way services are still conceived of. As mentioned above, the view that services are intangible goods is the orthodox position within the history of economics. One would have expected that by moving from object-preferences to actions-preferences, microeconomics would have moved correspondingly from the view that services are intangibles goods to the view that services are actions. But this did not happen: services are still treated as intangible commodities in contemporary microeconomic textbooks (Varian 1992, p. 314; Mas-Colell et al. 1995, p. 17). One also continues to apply to services the large panoply of concepts tailor-made for the economics of goods: thus services are said to be such that they can be had (Johnson 1958), be part of one’s endowment, be given up or received (as entailed by standard definitions of marginal rate of substitution) or be accumulated. But how could one have, be endowed with, give up, receive or accumulate actions? Thus, although the modern decision-theoretic approach to microeconomics de facto entails – correctly in our view – that fundamental exchangeables are actions, microeconomics continues to conceive of them as goods.
Why it that so? The main reason may simply be that the way to deal with goods exchanges under the hypothesis that basic exchangeables are actions remains obscure. To our knowledge, no encompassing view of exchanges amenable to subsume under the same heading exchanges of goods and exchanges of actions has been proposed so far (we shall advance one in Section 6). In lack of such a proposal, the only available way to explain goods exchanges is to revert back to the standard objectual conception of exchanges. As a result, the paradigm shift from good-driven to action-driven microeconomics remains incomplete. On exchangeables, to paraphrase Quine, economists tend to remain instinctively “goods-minded”.
Second, is the assumption that exchanges involve transfers of goods also standard? We noted that this is a very natural view to hold once exchangeables have been equated with goods, and it is unsurprisingly widely accepted. Menger speaks of “mutual transfers” (Menger 1976, p. 177–178); Fischer writes that “An exchange consists of two mutual and voluntary transfers, each in consideration of the other” (Fischer 1912, chap 1, Section 1: 3); more recently, Arnold writes that “Exchange, or trade, is the process of giving up one thing for something else” (Arnold 2016, p. 26); and Rutherford defines exchanges in terms of “The mutual transfer of goods, money or something of value between two or more parties” (Rutherford 2002, entry “Exchanges”).
Consider, finally, the view that exchanges are motivated by inverse valuations of goods. Is it widely shared as well? This way of putting it is admittedly quite Austrian. For instance, Wieser writes “Each of the two parties entering into a natural exchange desires to secure for himself superior value. Each surrenders something to which he attaches less utility-value than he does to the good or service which he obtains in exchange. […] it must happen that the two parties estimate the two objects of exchange in a directly opposite manner so that both may be able simultaneously to receive better value by the same transaction.” (Wieser 1927, p. 167 – similar Austrian descriptions are to be found in Menger 1976, p. 179–180, Böhm-Bawerk 1891, p. 179–180; von Mises 1949, p. 204–205; Rothbard 2009, p. 880–881; Kirzner 1960, p. 76; to which Wicksteed 1910, p. 126–157, may be added).
But even though the phraseology of “inverse valuation”, “reverse preference”, or “valuing goods in reverse fashion” is typically Austrian, the idea behind it – that, in any exchange, one prefers what one gets to what one cedes – is shared far beyond the Austrian heterodoxy. The idea is usually expressed in terms of mutual advantages: the reason why exchanges are mutually beneficial (ex ante, but no necessarily ex post), it is claimed, is precisely that each exchanger values the good of the other more than his own. Hence the exchangers expect to be better off by swapping goods.
The idea is already to be found in Aquinas: “buying and selling seem to be established for the common advantage of both parties, one of whom requires that which belongs to the other, and vice versa.” (Aquinas 1920, question 77, chap. 1). But the first complete formulation should perhaps be credited to Condillac: “Indeed, if one always exchanged equal value for equal value, there would be no gain to be made for either of the contracting parties. Now, both of them make a gain, or ought to make one. Why? The fact is that with things only having value in relation to our needs, what is greater for one person is less for another, and vice versa.” (Condillac 1776, chap. 6, p. 120). Following him, the French philosopher and economist Destutt de Tracy writes even more explicitly in 1823: “Whenever I make an exchange freely, and without constraint, it is because I desire the thing I receive more than that I give; and, on the contrary, he with whom I bargain desires what I offer more than that which he renders me.” (Destutt de Tracy 1817, chap. 1, p. 61–62). Such claims were still relatively rare and controversial at the time: Say 1855 (book I, chap. 2, p. 61) and Bastiat (1850, p. 66–72) strongly criticized Condillac’s view of the mutual benefits of exchange. But they became commonplace in the wake of marginalist theories. Here is Jevons:
Imagine that there is one trading body possessing only corn, and another possessing only beef. It is certain that, under these circumstances, a portion of the corn may be given in exchange for a portion of the beef with a considerable increase of utility. How are we to determine at what point the exchange will cease to be beneficial? […] if, to the trading body which possesses corn, ten pounds of corn are less useful than one of beef, that body will desire to carry the exchange further. Should the other body possessing beef find one pound less useful than ten pounds of corn, this body will also be desirous to continue the exchange. Exchange will thus go on until each party has obtained all the benefit that is possible, and loss of utility would result if more were exchanged. (Jevons 1888, p. 95–96, our italics).
This by now standard way of explaining not only why exchanges are mutually beneficial, but also at which point they will cease to be, by appealing to differences in the marginal utility of the exchangers is nothing less than a refined version of the inverse preferences idea. Exchanges of two kinds of goods between two individuals will carry on as long as an additional unit of the other’s goods has, for each exchanger more utility for him than the last unit of his own goods. Jevons’ proposal was reformulated 10 years later by Edgeworth through the introduction of indifference curves. His famous “box”, which vividly illustrates Jevon’s marginalist story above, is one place where the inverse preference story surfaces in textbooks of microeconomics. Although the idea that two individuals will gain from exchange as long as each continues to prefer something the other has to something he himself has is now typically couched in mathematical and technical terms – Edgeworth box, marginal rate of substitution – colloquial formulations of the idea have not disappeared. For instance, Marshall writes: “If each gives up that which has for him the lower utility and receives that which has the higher, each will gain by the exchange.” (Marshall 1920, chap. 5, Section 1). In their recent textbooks, Pindyck and Rubinfeld explain that “There is thus room for mutually advantageous trade because James values clothing more highly than Karen does, whereas Karen values food more highly than James does.” (Pindyck and Rubinfeld 2005, p. 603).
Finally, note that outside economics the same basic idea surfaces in philosophical writings. For instance, Reinach (1983, p. 3) writes: “Where two persons each have an object in their possession and each of the persons wants what the other has and is willing to give up his own thing for the sake of getting it, the immediate exchange of the things is the indicated way of satisfying the desire of both.” More recently Hardin (1982) characterizes economics exchanges in terms of “reverse valuation” and Brennan (2016) writes that “exchange is made possible by the fact that I have a greater desire for that which the other has (and I want) than for that which I have”.
The three central features of the STE – exchangeables as (i) goods which are (ii) mutual transferred and (iii) valuated in reverse fashion – are therefore assumptions widely shared, not only by Austrian economists, but in most of the historical and contemporary economics literature. We conclude that the view that exchanges are mutual transfers of goods motivated by inverse valuations thereof correctly captures the economists’ implicit, pre-theoretical conception of exchanges. We shall now raise two sets of objections against this theory.
3 The Incompleteness of the Standard Theory
3.1 What the STE Leaves Unexplained
Our first set of worries is that the STE leaves several intuitively important features of exchange unaccounted for. We only get a partial insight into the nature of exchanges. To reach a more complete account of exchanges, at least three points will need to be explained:
Bridging the gap. The explanatory step from inverse preferences (1) to mutual transfers (2) is incomplete as it stands. The preferences are held to motivate the transfers, but are clearly not sufficient to do so. Why should Julie’s preferring Paul’s money to her bike lead her to transfer her bike to Paul? Absent further explanation, such behavior seems plainly irrational: systematically transferring what we own and disprefer to those who own what we prefer is in general a very ineffective method to get us what we want. Paul is quite likely to take the bike and keep his money. So something must happen between (1) and (2) which makes it rational for Julie to transfer her bike to Paul so as to get his money.
The quid pro quo. A related worry is that the STE as it stands does not account for the quid pro quo of exchanges, the idea that things are exchanged against other things (Perry 1878, p. 76; Kirzner 1960, p. 76; Brennan and Pettit 2000, p. 82; Brennan 2016). What is missing in the STE is an understanding of the explanatory connection between the two transfers: Julie transfers her bike to Paul against Paul’s money. And likewise, Paul gives his money for Julie’s bike.
Claims and obligations. Another connected worry is that claims and obligations arise at some point in any exchange, and the STE leaves them unexplained. Suppose Julie transfers her bike to Paul, and that Paul goes away with the bike, without transferring his money to her. Surely, something has gone wrong: if they were indeed in the process of exchanging, Paul had at that point an obligation to transfer his money to Julie, and Julie had, conversely, a claim to Paul’s money since she already transferred her bike to him. It is only when the exchange is completed – when Paul has transferred his money – that such claims and obligation disappear. The STE per se does not explain the arising and vanishing of such transitory claims and obligations.
These points, we submit, are necessary features of our concept of economic exchange. If two individuals enter into some social interaction that fails to display any quid pro quo, or any correlative claims and obligations, they cannot properly be said to be exchanging.
3.2 Completing the STE?
Can the STE be completed so as to account for these three explananda? Some hints are to be found in Menger’s quote above. Menger adds that the individuals must “recognize” that they “value the goods in reverse fashion” (1976, p. 179–180). That is, the content of each exchanger preferences needs to be transparent to the other. Further, he adds that, once these inverse valuations of goods are mutually known, an exchange may occur “by mere agreement” of the parties (1976, p. 179). Shared knowledge and agreement may be thought to readily account for our three missing points. (1) The reason why Julie transfers her bike to Paul is that Paul has agreed to reciprocate by transferring his money to Julie. And both reach these agreements in virtue of knowing the preferences of each other. (2) The quid pro quo of exchange is also explained. Julie transfers her bike against Paul’s money because this is what she and Paul mutually agreed to be bound to. (3) Finally, the claims and obligations that arise and vanish through an exchange are simply the claims and obligations that would have remained unresolved had the agreement not been respected by one party.
However, supplementing the STE with shared knowledge and agreement in this way is problematic for three reasons.
First, shared knowledge of each other’s valuations of the goods at stake is quite demanding: for exchanges to take place, each party would have to have knowledge of the private, subjective preferences of the other. But, as Anderson (1993, p. 146) rightly observes, “Commodities are exchanged without regard for the reasons people have for wanting them”. Accordingly, on the more parsimonious theory we shall advance in the next section, the motivational gap is filled without requiring any exchanger to be aware of the other’s preferences.
Second, as we stressed above, and as agreed by Menger, the STE is meant to be compatible with methodological individualism. But it is controversial whether agreements are compatible. While agreements are often construed as exchanges of promises – which are individual acts–, Gilbert (1993) has argued that no exchange of promises can give rise to the sort of simultaneous and interdependent obligations that characterize agreements. Joint commitments lie according to her at the heart of agreements. If she is right, then plugging in agreement in the analysis of exchanges is incompatible with methodological individualism. The action theory of exchanges we shall propose below, by eschewing talk of agreements, avoids that potential incompatibility with methodological individualism.
Third, as Gilbert rightly urges, an agreement between two individuals amounts to an exchange of promises which generates two obligations, one for each individual. But, in most exchanges, only one individual incurs an obligation – as we shall see, the offeror. The offeree, on his side, incurs usually none (more on acceptance below). Intending to pay the amount indicated in the price tag (which is an offer) does not commit one to anything. Hence appealing to agreement in an account of exchanges not only threatens methodological individualism, it generates too many obligations and correlative claims.
In sum, the STE stands in need of completion in at least three respects and the main extant proposal for completing it proves unsatisfying.
4 The Restrictedness of the Standard Theory
Our second objection against the STE is more damaging: the STE fails to provide necessary conditions for exchanges. Many exchanges, we shall now argue, involve neither mutual transfers, nor inverse preferences. So the STE is at best true of only some exchanges. One of the main problems for the STE, we shall now argue, are exchanges of services.
The STE focuses on exchanges of goods. As we saw, to explain exchanges of services its upholders stress that “goods”, or “commodities”, encompasses more than material goods: “goods” also encompasses intangible goods, of which services are allegedly a sub-species.
We agree that there are intangible goods and that intangible goods can be exchanged: pieces of music, theories, the blueprint for a new car, computer programs, etc. are instances thereof.  We submit that rights (rights to use a good, financial claims ensuing from debts…) are another central case of non-tangible goods which can be exchanged. Julie can rent her bike to Paul for an hour, that is, exchange her right to use her bike during that hour against some money. Money is perhaps itself an intangible good (Smith and Searle 2003, p. 285–309). We disagree, however, with the idea that services are intangible goods. That “services are not intangibles” has been forcefully argued by Hill (1976, 1999). In what follows we shall argue that this is especially true in the case of exchanges of services: services cannot be transferred, and their exchanges cannot be motivated by inverse object-preferences.
4.1 Exchanges without Transfers
Consider first transfers. The act of transferring something is an episode involving three participants: the transferer, the transferee, and the thing transferred. A transfer unfolds in such a way that at the beginning the transferer has the thing and the transferee does not have it, whereas at the end the transferee has the thing and the transferer does not:
Transfer:x is transferred from y to z between t0 and t1 iff at t0x exclusively belongs to y and at t1x exclusively belongs to z.
An electron can thus be transferred from one atom to another. In the case of economic exchanges, the transfers at stake must be voluntary, and the “belonging” must be of the economically relevant kind, which we will assume here is ownership.  This definition of transfers puts two constraints on the kinds of entities that can be transferred:
transferable entities must be liable to enter into exclusive belonging relations with some other entities (the exchangers);
transferable entities must endure over time, at least during the transfer: the same x that was y’s at t0 must z’s at t1. 
As a consequence, if exchanges are defined in terms of transfers, as the STE has it, three kinds of goods cannot be exchanged:
episodic goods (services)
non-depletable goods (e.g. knowledge)
un-owned goods (granted rights).
Let us explain.
Episodic goods. Appealing to transfers in the definition of exchanges forbids exchanges of services. The reason is this: only endurants, that is, entities that persist over time without having temporal parts, can be transferred. Services, typically, either do not persist over time (the prescription of a remedy, the delivery of letter, the opening of a bank account are instantaneous – which is not to say that it does not take time to achieve them, or that they lack long-standing effects) or persist by having temporal parts (a violin lesson, a massage, a lawyer’s plea, visiting a cathedral). In both cases, services cannot be transferred because they do not keep their numerical identity over time, they do not endure. 
Furthermore, services might be provided or rendered, but they cannot be had or owned, as goods can. If Julie sells a biking lesson to Paul, it is not the case that there was a biking lesson that she had in the first place and that now belongs to Paul.
Non-depletable goods. The second restriction imposed by the appeal to transfers in the definition of exchanges concerns non-depletable goods, which we understand as goods such that their being owned by some agent do not decrease the amount of them available to other agents. Consequently, such goods might be transmitted to others without losing them. If Julie shares some of her knowledge to Paul in exchange for some money, she has not lost any of her knowledge once the exchange has taken place. Julie and Paul now both have this piece of knowledge in its entirety.  Likewise, if the young Julie gives her chickenpox to Paul against a doll, she still has her chickenpox after the exchange. The same is often true of transmission of digital data. Non-depletable goods can be transmitted without being lost. But since transfers require exclusive belonging, the STE cannot account for such exchanges. If we want to account for the exchange of non-depletable goods, we need a different relation to transferring in the third stage. Transmitting is a good candidate. Transmission is also a three-places relation. But, while something that is transferred is lost by the transferer, something might be transmitted without being lost by the transmitter. Compare transmitting some piece of knowledge to transferring a bike.
Un-owned goods. Finally, because transferring a good requires owning it first, the STE cannot accommodate cases of exchanges of un-owned goods. To the extent that rights are owned and endure over time, rights can be transferred. For instance, Julie can transfer to Paul – either forever or for some limited time – the right to use her bike. But, as urged by Reinach, transferring a right is not the only way to confer a right on another person: one might also grant that right to a person (Reinach 1983, Section 6, p. 68). Suppose Julie made a promise to Paul, and that, for whatever reason, she asks Paul for the right to revoke her promise. Paul might grant that right to Julie. But that granting, Reinach urges correctly, is not a transfer, for Paul never had the right to revoke Julie’s promise in the first place (only the promisor might have such a right). Thus, the right to revoke a promise is a right the promisee can grant, although he never had it. Besides, such un-owned rights clearly can be exchanged. Paul might grant to Julie the right to revoke her promise in exchange for Julie’s bike. Here again, we have an exchange without any mutual transfers.
Summing up: the STE only accounts for exchanges of enduring entities that can be owned. It could be replied that we have been attributing too strict a notion of transfer to the STE. Perhaps the STE can relax the concept of transfer it appeals to, so that it would encompass transfers in the strict sense (for goods), provisions (for services, e.g. playing the piano ), transmissions (for non-depletable goods, e.g. knowledge), and grantings (for un-owned goods, e.g. right to waive a promise). But it is, first, prima facie far from obvious that there exists a natural, non-disjunctive kind, which subsumes transfers in the strict sense, transmissions, provisions, grantings, and plausibly other cases. At any rate, it seems fair to say that at this point it is up to the STE’s upholder to tell us more about this broad kind. And, second, even if such a kind could be characterized, one would still need to show that it fits the other features of the STE. For suppose that transmitting knowledge is now considered as a kind of transfer. Is it at all plausible to say that, when Julie shares her knowledge of deontic logic with Paul against some money, she values her knowledge less than she values Paul’s money? Or suppose that rendering a service is considered as a kind of transfer. Is it at all plausible to say that when Julie sells a biking lesson to Paul she prefers Paul’s money to her biking lesson? Widening the concept of transfer beyond the clear cases of material and immaterial goods changing hands not only leads to a gerrymandered concept of transfers; it also violates the letter of the STE, which appeals to inverse valuations, as well as its spirit which is driven by the idea that economics is about allocating goods, conceived of as scarce resources.
4.2 Exchanges without Inverse Object-Valuations
In the same way that there are exchanges that do not involve mutual transfers, there are exchanges which do not involve any inverse preferences.
Exchanges made simply for pleasure constitute a first kind of counterexample. Such exchanges are often dismissed out of hand by upholders of the STE, who consider them rare borderline cases not worth spending too much time on (Menger 1976, p. 176, Böhm-Bawerk 1891, p. 190–194). Upholders of the STE are right that most exchanges are “not made simply for amusement”, in Böhm-Bawerk’s terms (1891, book 4, chap. 1). But as long as some exchanges are pleasurable, however, rare they may be, a good theory of exchange should accommodate them. The STE fails to account for such exchange for two reasons. First, the preferences involved in exchanges made for amusement are not directed at goods, but at the action of transferring goods. Second, when two children exchange two toys back and forth, their preferences are not opposite but convergent: both prefer transferring toys mutually over not transferring toys mutually.
But the most important class of counterexamples to the claim that exchanges are motivated by inverse preferences about the exchangeables are, again, exchanges of services. Suppose Julie explains modal logic to Paul in exchange for Paul’s playing the violin to her. Should we say, as entailed by the STE, that Julie values Paul’s playing the violin to her more than she values explaining modal logic to him? And that, on the other hand, Paul prefers Julie’s explaining modal logic to him to playing the violin to Julie? That sounds very weird. If anything, Paul and Julie have converging preferences: both of them prefer a situation where Julie explains modal logic to Paul and Paul plays the violin to Julie to a situation where none of these two events happens. Such preferences or valuations are clearly not opposite but convergent (more on this below).
The point is perhaps even more obvious in the case of mixed exchanges, where a good is exchanged against a service. Suppose Julie transfers her bike to Paul in exchange for Paul’s playing the violin to her. One might, perhaps, make sense of the idea that Julie prefers Paul’s playing the violin to her bike. But it would be quite contrived to say that Paul prefers Julie’s bike to his playing the violin for her.
The intuition of opposite valuations works well for goods, but vanishes once services are taken into consideration. This is not to say, nor to imply, that no preference is at stake here, nor that the idea of exchanges being mutually beneficial is misguided. On the contrary, we shall argue that all exchanges involve valuations, preferences – albeit convergent ones – in virtue of which they are mutually beneficial (not only ex ante, but also ex post). Our point has only been that neither mutual transfers nor inverse preferences hold true in the case of exchanges of services. 
This confirms that, as argued by Hill, it is a bad mistake to equate services with intangible goods. The STE has no problem dealing with exchanges of such intangible goods (suppose Julie exchanges her right to use her bike against Paul’s right to attend a concert: we have got mutual transfers of rights and inverse preferences about these rights). But the STE cannot deal with exchanges of services. The more it treats services as goods – that is, as objects which one refers to, which can be owned, transferred, and towards which we entertain objectual attitudes – the more it is led to absurd conclusions of the above kind. While there are clearly intangible goods (transferable rights, for instance), the distinction between tangible and intangible goods does not dichotomize exchangeables. This is the reason why, in order to capture exchanges of services, the theory of exchange needs to accept exchangeables which are not goods.
Services, we submit, do not belong to the category of objects, but to the category of actions. A service is something one does for somebody, not something one transfers to somebody. Bracketing vexing issues, actions are not primarily referred to: they are basically expressed through verbs and propositions, not names. Correspondingly, our attitudes towards actions are typically propositional, not objectual. Not: preferring x to y; but: preferring to ϕ rather than to ψ. Not: liking x more than one likes y; but: liking to ϕ better than liking to ψ. Actions cannot be owned in the strict sense, they do not endure over time, and therefore cannot be transferred. Yet they can be exchanged. They are even, as we shall now argue, the most fundamental exchangeables.
5 The Action Theory of Exchanges
In order to avoid the problems faced by the STE, we proceed as follows. To get a complete theory of exchange, we introduce offer and acceptance. To get an unrestricted theory of exchange, able to account for exchanges of services, we argue that even in the case where goods are exchanged, what is immediately exchanged are actions. One consequence of focussing on actions rather than goods is that the motivating preferences are convergent rather than inverse.
The view that actions are the target of exchanges is not unprecedented. It was endorsed by Frederic Bastiat, who insisted that all exchanges (which are for him the fundamental social phenomena) are fundamentally exchanges of services: “every transaction can be reduced to a bartering of services” (1851, p. 106, see also, p. 31–33, 63, 74–75, 115). Unfortunately, perhaps because Bastiat combined his approach to exchanges with a disputable theory of economic value,  his proposal has remained widely neglected. One exception is his American disciple Arthur Latham Perry, who builds upon Bastiat’s proposal to develop a plausible threefold classification of exchangeable entities (commodities, claims and services), arguing that the latter are the most basic (Perry 1878, p. 84–87).
The action theory of exchange we shall now propose takes up Bastiat’s central proposal: what we basically exchange are not goods (which fall under the category of objects) but services (which, as just argued, fall under the category of actions). This is the first respect in which our theory departs from the STE. The second respect is that the action theory introduces social acts, namely offers and acceptances, at the heart of exchanges.
Let us introduce this action theory by looking at how it deals with our earlier example of exchange of services: Julie explains modal logic to Paul in exchange for Paul’s playing the violin to her iff:
Julie prefers [to explain modal logic to Paul and that Paul plays the violin to her] rather than that none of these actions take place. Paul has a preference with basically the same content: he prefers [to play the violin to Julie and that Julie explains modal logic to him] rather than none these actions take place.
Furthermore, Julie believes that making an offer to Paul is a way for her to get Paul to play the violin to her.
Because of her preference and her belief, Julie makes the following offer to Paul: “I promise you that if you play the violin to me, I will explain modal logic to you.”
Because of his preference, Paul accepts Julie’s offer and plays the violin to her. Julie now incurs, in virtue of her promise, the unconditional obligation to explain modal logic to Paul, which she does, thereby settling the exchange.
The action theory of exchange is a generalization of this story:
Action theory of exchanges (ATE): Individuals A and B respectively ϕ and ψ in exchange=df
Preferences and belief:
A prefers [to ϕ and that B ψ-s] rather than [not to ϕ and that B does not ψ]
B prefers [to ψ and that A ϕ-s] rather than [not to ψ and that A does not ϕ] 
A believes that [promising to ϕ to B on the condition that B ψ-s] is a way for him to make B ψ.
Offer and acceptance:
The offer: Because of (1.1) and (1.3), A promises to B that he will ϕ, if B ψ-s.
The acceptance: Because of (1.2), B accepts the offer.
First provision. Because of (2.2), B ψ-s. As a result, A incurs the obligation to ϕ.
Second provision. Because of (2.1) and (3.1), A ϕ-s.
Or the reverse: (1.3′): B believes that promising to ψ to A on the condition that A ϕ-s is a way for him to make A ϕ; hence: (2.1′) B promises to A that he will ψ, if A ϕ –s; (2.2′) A accepts B’s offer; (3.1′): A ϕ –s; (3.2′) B ψ-s.
Let us comment on and motivate these conditions in turn.
5.1 Preferences and Beliefs
The first stage only involves each party’s private mental states: each has a preference of a given sort, and at least one of them has a belief on how to satisfy that preference.
With respect to the preferences (1.1) and (1.2), four comments are called for.
First, under the ATE, the preferences essential to exchanges are directed at the actions of the exchangers (transferring the bike/the money), rather than at their goods (the bike, the money). The first reason in favor of this move, as we saw, is that it paves the way for a unified account of the exchanges of goods and services. A second reason in favor of this focus on actions is that it connects preferences more tightly with the content of offers and acceptances, and that of provisions: the very same actions that are preferred in the first step are promised in the second step and performed in the third step. In the STE by contrast, there was a motivational gap between preferences and transfers. No such gap impairs the ATE.
Second, it should be noted that the preferences appealed to in the ATE do not represent the whole of A and B’s preferences with respect to the actions at stake. Typically, each exchanger prefers most to get what he wants without having to give anything, and prefers least not to get what he wants while nevertheless giving something. Thus the whole ordering of A and B’s preferences will typically be:
A’s preferences: [A does not ϕ and B ψ-s]>[A ϕ-s and B ψ-s]>[A does not ϕ and B does not ψ]>[A ϕ-s and B does not ψ]
B’s preferences: [A ϕ-s and B does not ψ]>[A ϕ-s and B ψ-s]>[A does not ϕ and B does not ψ]>[A does not ϕ and B ψ-s]
When we say that A and B’s preferences are convergent we only mean the preferences that are here in bold. It is not the whole sets of the exchangers’ preferences that are convergent, but only the sub-sets of those that motivate the exchange.
Third, why not use “that clauses” all over instead of that mixture of infinitive complements and that-clauses? That is, why not say:
A prefers (that A ϕ-s and that B ψ-s) rather than (that A does not ϕ and that B does not ψ)
B prefers (that B ψ-s and that A ϕ-s) rather than (that B does not ψ and that A does not ϕ).
Our main reason for not retaining this simpler phrasing is that one of the actions that each party prefers is an action that he identifies as an action of himself, which the that-formulation above fails to capture. Applying Perry (1979)’s problem of essential indexicals to preferences, A might prefer that A ϕ-s, without realising that he is A. The problem does not arise with “A prefers to ϕ”. This issue will presumably often be ignored for formalisation’s sake: going for that-clauses all over is far simpler. However, such a simplification, we want to stress, is not part of the theory of exchange itself.
Fourth, one complication that our proposal does not take into account as it stands is that in many (plausibly most) cases of exchange, the contents of the preferences, as well as the contents of the offers, should be expressed by general instead of singular propositions. The preferences will often be of the form:
A prefers (that he does ϕ and that someone does ψ) rather than (that he does not ϕ and that nobody does ψ)
B prefers (that he does ψ and that someone does ϕ) to (that he does not ψ and that nobody does ϕ)
How to plug-in generalized preferences in the ATE is a question we here leave open.
Finally, one chief point with respect to preferences motivating exchanges is that under the ATE these preferences are convergent rather than inverse (as per the STE), which means that exchangers exchange because they both value the same course of action against the same alternative course of (in)action.
(1.3) The belief. We now have two agents with weakly converging preferences: there is a course of action which both prefer to alternative ones. In our example, both Julie and Paul prefer the course of action in which Julie explains modal logic to Paul and Paul plays the violin to Julie. How do we move from these converging preferences towards the exchange? Although the preferences of the parties are private, their expression or disclosure is not required in order for Julie and Paul to move on to the next stage. All that is needed to go further, we submit, is an offer from one of them to the other. In order to make such an offer, one party must have, on top of his preference, a belief. In order to make an offer to Paul, Julie must believe that making such an offer is likely to bring her the money transfer she wants. If, on top of her preference, Julie believes that offering to explain modal logic to Paul if he plays the violin to her is a way to get Paul to play the violin, she may well proceed with making this offer (Paul might not have any belief of the sort).
Although Julie’s instrumental belief might stem from some beliefs or guesses regarding the other party’s own preferences, they do not have to. Julie’s belief that Paul might accept her offer is often justified by her attributing to Paul some preference for her explaining modal logic to him. But there is no necessity to speculate about the other agent’s preferences in order to rationally make an offer to him. Surely, Julie needs to believe that her offer has a chance of being accepted by Paul in order to make it to him. But she does not need to believe that he prefers her explaining modal logic to him in order to offer to explain modal logic to him in exchange for him playing the violin to her. This is because she does not need to know what might prompt him to accept her offer in order to make such an offer. An economic agent conditioned purely behaviorally, lacking any theory of mind, could still rationally proceed to make an offer. “Making some kind of offers happens to get me what I want. I have no clue about why this is so, but this works”.
Besides, even when Julie’s offer is motivated by her ascribing some preferences to Paul, Paul’s acceptance will often remain blind to Julie’s own preferences: typically, only the offer will matter to him, regardless of its underlying motivation. So neither exchanger needs to inquire about the other’s preferences in order for the exchange to take place.
5.2 Offer and Acceptance
(2.1) Following Bach (1995),  we assume that offers are promises with conditional content. There is a distinction between unconditional promises with conditional content (I promise that if p, I ϕ), and conditional promises (If p, I promise that I ϕ).  Offers are of the former kind: promises with a conditional content. Julie promises to Paul to transfer the ownership of her bike to him if he transfers to her the ownership of some amount of money. Because of this offer, Julie incurs an obligation to transfer her bike to Paul if he pays her. Julie’s offer may be that she promises to transfer her bike to Paul if he pays her now. But she may alternatively offer Paul the possibility to pay later. In such a case, Julie promises to transfer the bike to Paul now, if Paul promises now to pay her later. In that case, the action that is exchanged against Julie’s transfer of her bike is Paul’s promise to pay rather than Paul’s payment itself.
Following Reinach’s (1983) pioneering and all too neglected work, we here assume that promises have at least the two following essential features:
Promises are social acts in the sense that they are uttered by a promisor, and have to be heard and understood by the promisee.
Promises generate, in virtue of their nature, pro tanto obligations on the promisor to realize their content, and correlative pro tanto claims for the promisee. 
That is, necessarily, in virtue of the nature of promises, if A promises to ϕ to B, then (1) B heard and understood A’s utterance (ii) as an immediate result of this promise, A incurs the obligation to ϕ and B incurs the correlative (same content) claim to A’s ϕ-ing. In the case of promises with conditional content, the obligation of the offeror and the related claim of the offeree also arise at the very moment the offer is made, but both are conditional: the offeror has an obligation to ϕ if some condition is met; and the offeree has the correlative conditional claim to the offeree’s ϕ-ing. Both the obligation and the claim are actual, but unactivated, as it were, waiting for the fulfillment of the condition in order to become unconditional.
One might object that many exchanges occur without any offers having been made. This however neglects the fact that many offers remain implicit or tacit. Price tags, for instance, constitute one ubiquitous form of offer (no to be conflate with prices, which, contrary to price tags, are determined by the exchanges actually taking place).
Another possible objection is that the preference of the offeree is often not fixed before the offer. Offers might prompt new preferences or change the preferences of offerees. We entirely agree: it could be that Paul did not have a preference for buying Julie’s bike before receiving Julie’s offer. Although the linear presentation we have adopted might suggest the contrary, the ATE, we wish to stress, is not committed to the offeree’s preferences being fixed before the offer. All that it requires is that the offeree accepts the offer because of his preference. This does not rule out the possibility that the offer elicited the offeree’s preference.
(2.2) Acceptance: once Julie makes her offer, the ball is in Paul’s court. It is up to him to accept the offer or not. In the present context, accepting an offer is not simply uptaking it (that is, hearing it, grasping it), nor is it simply expressing one’s intention to realize the condition. There are two possibilities:
To accept an offer may consist in performing another social act, such as the unconditional promise to fulfil the condition of the offer, as argued by Bach (1995). To accept Julie’s offer to provide him with the bike if he pays her, would be for Paul to promise to pay her.
To accept an offer may be simply voluntarily fulfilling the condition specified in its content. Accepting an offer conditional on a payment might just be putting the money on the table. In this case, the act of transferring counts as both an acceptance of the offer and as the fulfillment of the condition, thus activating A’s obligation to actually fulfil his offer. The acceptance (2.2) and the first provision (3.2) are one and the same.
We suspect that the last answer is the correct one, and that the intuition in favor of the first answer stems from a confusion between offers conditioned on payment and offers conditioned on promises of payment. These two kinds of offers give rise to two very distinct sorts of exchanges. Suppose Julie promises Paul to explain modal logic to him if Paul pays her a certain amount of money. The ensuing exchange will be an exchange of a lesson of modal logic against a certain amount of money. Suppose, on the other hand, that Julie promises to Paul to explain modal logic to him if Paul promises to pay a certain amount of money to her. Such an exchange will typically be an exchange of a lesson of modal logic against a claim to a certain amount of money (by contrast to an exchange against a certain amount of money). What Julie has earned after the second exchange is a financial claim (i.e. the right to receive money latter) rather than some money. Such a claim does not need to be met for the exchange to have taken place. Debts are exchanged in financial markets, whether or not these debts will be repaid. Offers conditioned on transfers of goods are distinct from offers conditioned on promises of transfer of goods.
With this distinction in hand, our proposal is that promises constitute acceptances only in the latter case, that is, the case of offers conditioned on promises. Not all acceptances are promises; only acceptance of offers conditioned on promises are. Thus in any case, accepting an offer is just fulfilling its condition.
Still, one might object, is not it perfectly fine for Paul to accept Julie’s offer to explain modal logic to him against a payment just by promising to pay her? Admittedly, on the face of it, it is quite common to accept offers whose conditions cannot be fulfilled immediately (such as important payments) by promising to fulfil these conditions later. But such cases, we submit, should not be taken at face value. The reason for this is that, when Paul replies to Julie’s offer by saying “I accept, I will pay you by tomorrow”, it would perfectly correct for Julie to retort, without violating any of her promissory obligations, “No credit given, I want a payment, not a promise thereof”. Were Paul’s promise to count as an acceptance, Julie would be refusing Paul’s acceptance of her offer, which she is not entitled to do (the best she can do is to revoke her promise – to retract her offer – but for this, as we saw in Section 4.1. Paul has to grant her the right to revoke).
What then, really happens in cases where offers conditioned on payments are seemingly accepted through promises of payment? At least two readings are possible.
First, it might be that the offer was implicitly conditioned on a promise of payment, so that the promise is indeed an acceptance of that implicit offer. How an offer explicitly conditioned on a payment may actually count as an offer conditioned on a promise of payment is, we surmise, easily explained through conversational implicatures. For instance, in cases where a large amount of money is in play it usually goes without saying that the money cannot be transferred right away.
Second, if the initial offer was fully explicit and not implicitly conditioned on any promises to pay, the offeree’s promise to pay might constitute a counter offer instead of an acceptance. Julie’s offer was to explain modal logic to Paul against a payment. Paul does not accept that offer, but instead makes the following counter offer: he promises Julie that, if she explains modal logic to him, he will pay her. It is now up to Julie whether to accept that offer or not. In such a case, some other intermediary steps would have taken place between the first offer (2.1) and the acceptance of the final offer (2.2), namely, a negotiation. Admittedly, while exchanges often involve such turnarounds, these are not essential components of them.
(3.1) Before the condition specified in Julie’s offer has been fulfilled, Paul’s claim and Julie’s related obligation remain conditional, un-activated. But, once Paul has played the violin to Julie, his claim to Julie’s logic lesson, together with Julie’s obligation to provide such a lesson, become fully actual and unconditional.
(3.2) These two correlative claims and obligations are met and disappear once Julie explains modal logic to Paul. The exchangers are then finished: once an exchange has been completed, all the obligations and claims which arose during it are resolved. The claims and obligations generated within exchanges are transient.
We shall now argue that the ATE fares better than the STE.
6 Exchange of Goods with the ATE
We argued that the STE, because it is tailor-made for exchanges of goods, cannot account for exchanges of services. Now our own ATE faces a symmetrical objection: since it is modeled on exchanges of services, one should worry that it cannot account for exchanges of goods. Given the central role that good exchanges play in economics, the sheer denial of their possibility would clearly be a reductio of the ATE.
At this point one might be tempted to doubt that any theory of exchange will be in a position to subsume exchanges of services and exchanges of goods under the same heading. Such a disjunctive line of thought naturally suggests itself once we take the measure of the categorial distinction, emphasized above, between goods and services. Tempting as it, this disjunctive approach to the concept of exchange should however be resisted for one simple reason: goods can be exchanged against services. There must therefore be one overarching concept of exchange, which subsumes goods-for-goods, services-for-services and services-for-goods exchanges. This, we maintain, is the category of exchanges of actions, from which the category of goods-exchanges can be defined, as we shall now argue.
A natural way to fit exchanges of goods into the ATE would be to equate exchanges of goods with exchanges of transfers of goods. To go back to our opening example, Julie sells her bike to Paul iff:
Julie prefers [to transfer the ownership of her bike to Paul and that Paul transfers the ownership of his money to her] rather than that none of these transfers happen. Paul has a preference with basically the same content: he prefers that [the two transfers take place] rather than not.
Furthermore, Julie believes that making an offer to Paul is a way to get Paul transfer the ownership of his money to her.
Because of her preference and of her belief, Julie makes the following offer to Paul: “I promise you that, if you transfer the ownership of your money to me, I will transfer the ownership of my bike to you.”
Because of his preference, Paul accepts Julie’s offer and transfers the ownership of his money to Julie. Julie now incurs, in virtue of her promise, the unconditional obligation to transfer the ownership of her bike to Paul, which she does, thereby settling the exchange.
Exchanges of goods (first try): Individuals A and B exchange goods x and y iff:=df
Preferences and belief:
A prefers [to transfer the ownership of x to B and that B transfers the ownership of y to him] to [not to transfer the ownership of x to B and that B does not transfers the ownership of y to him]
B prefers [to transfer the ownership of y to A and that A transfers the ownership of x to him] to [not to transfer the ownership of y to A and that A does not transfers the ownership of x to him]
A believes that promising to B to transfer the ownership of x to B on the condition that B transfers the ownership of y to him is a way for him to get B transfer the ownership of y to him.
Offer and acceptance:
The offer: Because of (1.1.) and (1.3), A promises to B to transfer the ownership of x to B on the condition that B transfers the ownership of y to him.
The acceptance: Because of (1.2), B accepts the offer. Hence, B incurs the obligation to fulfil the condition specified in A’s promise: B ought to transfer the ownership of y to B.
First provision. Because of (2.2), B transfers the ownership of y to A. As a result, A incurs the obligation to transfer the ownership of x to B.
Second provision. Because of (2.1) and (3.1), A transfers the ownership of x to B.
Or the reverse (…)
There are however strong reasons to reject this proposal. Exchanging transfers of goods is necessary but not sufficient to exchange goods. To see this, consider the case of exchanges made simply for amusement. Such exchanges, we argued (Section 4.2.), are motivated by preferences bearing on the actions of transferring, rather than by preferences bearing on the goods exchanged. What the exchangers really exchange (and enjoy) are not goods, but actions of transferring goods. Our point was that the STE, with its inverse object-preferences, could not accommodate such exchanges, because the preferences motivating them are convergent.
Now this objection to the STE backfires against our ATE in the present context. If exchanges made for amusement are ultimately just exchanges of actions and not exchanges of goods, then some exchanges of transfers of goods are not exchanges of goods. More generally, although the reason we are interested in being transferred a good is most often that we are interested in the good, it does not have to be so. Paul might want to buy Julie’s bike not because he has any interest in the bike, but just because he thinks this is his best way to come into contact with Julie or to spend some time with her. Object-preferences cannot be scrutinized from preference over transfers of object.
Thus, unless there is a way to discriminate, within exchanges of transfers of goods, between those that are simply exchanges of transfers and those that are really exchanges of goods, the ATE fails to capture what is specific about goods exchanges.
To answer this important worry, we propose utilizing the STE’s own arsenal. To distinguish between exchanges of transfers of ownership of goods simpliciter and genuine exchanges of goods we suggest appealing to the preferences that ground the preferences for transfers. The idea is that what distinguishes mere exchanges of transfers of goods from exchanges of goods is that, in the latter but not the former case, the preferences for transferring the ownership of goods are grounded in the opposite preferences for goods. This is the important grain of truth in the STE. We thus need to supplement our previous account of goods exchanges by inverse object valuations (added conditions in bold):
Exchanges of goods (second try): A and B exchange goods x and y iff:
A prefers y to x
B prefers x to y
Preferences and belief:
Because (0.1), A prefers [to transfer the ownership of x to B and that B transfers the ownership of y to him] to [not to transfer the ownership of x to B and that B does not transfers the ownership of y to him]
Because (0.2), B prefers [to transfer the ownership of y to A and that A transfers the ownership of x to him] to [not to transfer the ownership of y to A and that A does not transfers the ownership of x to him]
A believes that promising to B to transfer the ownership of x to B on the condition that B transfers the ownership of y to him is a way for him to get B transfer the ownership of y to him.
Offer and acceptance:
The offer: Because of (1.1) and (1.3), A promises to B to transfer the ownership of x to B on the condition that B transfers the ownership of y to him.
The acceptance: Because of (1.2), B accepts the offer. Hence, B incurs the obligation to fulfil the condition specified in A’s promise: B ought to transfer the ownership of y to B.
Second provision. Because of (2.1) and (3.1), A transfers the ownership of x to B.
Or the reverse (…)
Thus, in the case of exchanges made for pleasure, exchangers do not care about the goods at stake: what they value is the activity of transferring. Their preferences for transfers are not grounded in inverse preferences for goods, conditions (0.1) and (0.2) are not met. Accordingly, goods are here mere decorations, and all we have is an exchange of services (namely, of transfers).
If, on the other hand, the exchangers prefer to transfer the ownership of their goods because they prefer each other’s goods, then we have an exchange of goods. When exchanges of transfers of ownership of goods are ultimately grounded in reverse preferences for these goods, then is it is right to say that these goods are exchanged. Note, incidentally, that this story typically holds for offers conditioned on promises, discussed above. Such offers typically prompt exchanges that are not exchanges of services (promises), but exchanges of a special kind of goods: claims. This is because the reason why we usually accept a promise in return for, say, the transfer of a good, is that we value promises made to us in virtue of the claims they give rise to. When Julie transfers her bike to Paul in exchange for Paul’s promise to pay her, what she really is after is not Paul’s promising per se, but the claim that the promise gives rise to. The two goods exchanged are here the (promise-generated) claim and the bike.
This strategy of identifying the target of exchanges via the preferences that ground the preferences for transfers yields two interesting refinements.
First, building on Commons (1931), there is a distinction between valuing goods and valuing ownership of goods. These valuations usually go together: we often prefer the good that we prefer to own. But this does not need to be so. Julie might prefer her castle to Paul’s house, but nevertheless prefer owning Paul’s house to owning her castle (because, say, maintaining the castle it too costly). Paul, on the other hand, might prefer his house to Julie’s castle, but nevertheless prefer owning Julie’s castle to his house (because, say, his house is in a country in which he has fiscal troubles). In such a case, Paul and Julie might end up exchanging the ownership of their house and castle. However, the targets of their exchange are not the castle and the house, but rather the ownerships of the castle and of the house. More generally, if the exchangers prefer to transfer the ownership of their goods because they prefer to own each other’s good, and they do not prefer each other’s good, we have an exchange of ownership of goods which is not an exchange of goods owned.
Second, whether an exchange is ultimately an exchange of goods, an exchange of ownership, or just an exchange of transfers, is dependent on each exchanger’s motivation. Since these intrinsic motivations need not be the same, one and the same exchange can be both an exchange of goods relative to one exchanger and a pure exchange of action relative to the other. Suppose Julie transfers her bike to Paul against some money because she values Paul’s money more than her bike, and that Paul transfers her money to Julie against her transferring her bike to him, because he simply loves transacting with Julie. This single exchange proceeds from two very different motivations: for Julie, the exchange is ultimately motivated by intrinsic object preferences; for Paul, it is fundamentally motivated by action preferences. This very same exchange will be an exchange of goods with respect to Julie, and a simple exchange of services with respect to Paul.
In sum, by introducing object preferences (which upholders of the STE appeal to) as possible grounds for the action preferences (on which the ATE relies), the ATE is in a position to distinguish between exchanges of goods, exchanges of ownership of goods, and pure exchanges of transfers of ownership of goods, although all these exchanges essentially require exchanges of transfers of ownership of goods.
7 Wrapping up: STE vs. ATE
We raised two kinds worries against the STE.
Incompleteness. First, the STE is incomplete in three respects: (i) there is a motivational gap between inverse object preferences and mutual transfers, (ii) the quid pro quo of exchanges–exchanging something against something else–is left unexplained, (iii) the claims and obligations that arises within exchanges remain ungrounded.
The ATE avoids all these flaws: (i) The motivational gap is filled since the preferences motivating exchanges bear on the very actions constitutive of exchanges, which also figure in the content of the offer, (ii) the quid pro quo of exchange is accounted for by offers (understood as promises with conditional content), and their acceptance: A conditionally promises to ϕ in order to get B to ψ, and B ψ-s in order to get A to ϕ, (iii) the claims and obligations that arise within exchanges are simply the promissory claims and obligations that arise from any promise.
It might be objected that the ATE too comes with its own gaps. First, one might think that a key ingredient missing from the ATE is trust. To accept Julie’s offer, Paul needs to trust Julie’s description of the bike, and he also needs to trust that she will fulfil her promise and give him her bike after having received the price-tagged amount of money. Trust is indeed often required for an offer to be accepted, and therefore for an exchange to take place. But that does not entail that trust is an ingredient of exchanges. A first reason for this is that interpersonal trust may not always be necessary. Perhaps Paul does not trust Julie, who he considers to be very unreliable, but nevertheless accepts her offer because he counts on the legal institutions to enforce the rights and obligations arising from promises. For this he may need to trust the institutions at stake, but this is a very different kind of trust than trust directed at the promisor. Other cases are imaginable: it is not the task of a general theory of exchange, we submit, to elucidate and spell out the various possible pre-conditions of acceptances.
Likewise, one may worry that the ATE neglects another core aspect of exchanges, namely, their various degrees of voluntariness. Often a preference for exchanging exists only because one party in the exchange feels compelled to carry out the exchange, typically because of asymmetries in bargaining power. Extreme cases are the so-called “offers one cannot refuse”, such as ‘Your money or your life’. Our response here, again, is that, in the same way that a theory of exchange does not need to incorporate the pre-conditions of offers and acceptances, a theory of exchange does not need to elucidate the origin of the agents’ preferences.  This way, the theory of exchange remains compatible with all the varieties of genetic explanations of agents’ preferences, from coercion to autonomous deliberation. Correspondingly, the many normative issues raised by blackmail, coercive offers, unequal or exploitative exchanges should not be settled by a theory of the nature of exchange. If one is to disagree about whether or not there are exploitative exchanges, or about whether or not they should be regulated, one needs first to agree about what exchanges are.
Restrictedness. Our second objection to the STE was that it is unable to account for exchanges of services, because both the preferences and the actions (transfers) it appeals to bear on objects, and because it assumes that such preferences are inverse, which does not hold true of services. No such problem arises within the ATE. When Julie explains modal logic to Paul in exchange for Paul’s playing the violin to her, no transfer ever takes place: the ATE takes services for what they are, actions, and does not need to consider them as intangible goods passing from hand to hand. Preferences, being propositional, do not need to be interpreted as bearing on hypostasized actions. Further, because the preferences are convergent, the ATE conforms to our intuitions that, in the case of exchanges of services, it is not the case that one exchanger values more what the other values less.
Finally, while the STE fails to account for exchanges of services, the ATE can use inverse valuations to account for exchanges of goods.
However, one may ask, could the STE not fare better than the ATE in other respects?
Methodological individualism. One purported advantage of the STE noted in Section 2 is its compatibility with methodological individualism. One might worry that, by putting social acts (offers) at the heart of exchanges, the ATE, for its part, proves incompatible with methodological individualism: some form of collective intentionality or joint action would be nested within all exchanges.
This worry is misguided. Social acts indeed require more than one individual – as opposed to solitary actions, such as intending, grieving, or running – but they do not require collective agents or thinkers. Other people are essential to social acts not because they jointly perform them but only because they hear them. The promise that Julie makes to Paul has to be heard, and understood, by Paul (Reinach 1983, p. 109). But, while its uptake by Paul is essential to Julie’s promise being made, Julie is the only agent that makes the promise. Thus, although any social act requires two persons at least, they remain the act of one person only. No we-promises are required by the theory: only I-promises and I-uptakes.
Value subjectivism. Another noted feature of the STE is its value-neutrality: exchanges, on the STE, are only motivated by subjective-valuations of individuals, and no commitment to objective values is required to account for exchanges. One might fear that the ATE is, in contrast, too normative. Because each promise generates an obligation on the part of the promisor to keep his promise, and a claim to the same effect on the part of the promisee, objective norms enter the scene. After the offer, the offeror incurs a conditional obligation (A has the obligation to transfer x if B transfers y to A), and the offeree has a conditional claim (B has a claim to the transfer of x if B transfers y to A). After the offeree’s acceptance these norms become non-conditional: A has the non-conditional obligation to transfer y to B, and B a non-conditional claim to the same effect. All these norms are objective: neither figure within the scope of an attitude. It is not that Julie thinks she has an obligation; she really has one, whether she recognizes it or not. And the same hold for Paul’s claim. So, according to the ATE, exchanges are norms-laden from the second-step on.
We submit that, while this is true, it is harmless. The crucial thing is that no normative assessment of the preferences of the individuals is involved in this picture. Nowhere is it claimed that individuals should prefer x to y, or that it would be (rationally, ethically, esthetically…) better to prefer x to y. To the extent that an assessment of preferences is, according to the principle of value-neutrality, what economic science purports to avoid, the ATE is as value-free as the STE.
Mutual gains. Under the STE, the mutual gains from exchanges are grounded in the exchanges’ satisfying the inverse object preferences of the exchangers. Paul values Julie’s bike more than his money; Julie values Paul’s money more than her bike. Hence, exchanging the bike against the money would satisfy them both. Under the ATE, exchanges are also mutually beneficial, but for a rather trivial reason. The preferences at stake are not opposed, but have (nearly, as we saw) the same content: both Paul and Julie prefer that Paul transfers the bike to Julie and that Julie transfers the money to Paul to the situation in which neither of these transfers take place. Hence, under the ATE, the mutual gains from exchanges are grounded in the exchanges’ satisfying the convergent propositional preferences of the exchangers. Note that while, on the STE, exchanges are mutually beneficial ex ante, this is not essentially the case on the ATE, because the preferences that an exchange satisfies bear on the very actions constitutive of the exchange (there is not motivational gap). It is not because the exchangers expect (correctly or not) to be better off after the exchange that exchanges are mutually beneficial (although this might also be the case); more fundamentally, but also more trivially, it is because the exchangers are willing to exchange that exchanges satisfy them.
Grammaticality. Finally, one might think that, contrary to the STE, the ATE achieves generality at the price of violating the syntax of “exchange”. The verb “to exchange” usually takes four referring expressions (in italics) to make a sentence:
Julie and Paul exchange a bike for an amount of money.
“Exchanging” is an n-place predicate. While the STE got this right, the ATE, appears to entail an ungrammatical construal, where “exchange” functions (partly) as a connective taking sentences:
*Julie and Paul exchange that Julie transfers her bike to Paul for that Paul transfers his bike to Julie.
Our reply is that not all uses of the term “exchange” are predicative. The locution “in exchange” takes sentences. We suggest that, with respect to the nature of exchanges, it constitutes the fundamental form:
Julie transfers her bike to Paul and, in exchange, Paul transfers his money to her.
On the whole, with respect to methodological individualism, value subjectivism, mutual advantages and grammaticality, the ATE fares at least as well as the STE. And it clearly fares better than the STE in providing sufficient conditions for exchange and in accounting for exchanges of services.
To conclude, the distinction between exchanges of goods and exchanges of services is uncontroversial. The difficulty is to understand how they relate. The STE tackles this issue by treating exchanges of services as a special case of exchanges of goods. We have argued that this strategy is doomed to failure. What should be done is exactly the opposite: consider exchanges of goods as a special case of exchanges of services. In accordance with Bastiat, exchanges of services, not exchanges of goods, constitute the most fundamental kind of economic exchanges. 
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