The B.E. Journal of Theoretical Economics

Published by De Gruyter

Volume 20 Issue 1 -

January 2020

Issue of The B.E. Journal of Theoretical Economics

Contents
Journal Overview

Research Articles

June 9, 2018

Optimal Forestry Contract with Interdependent Costs

Francis Didier Tatoutchoup, Paul Samuel Njiki

Article number: 20160058

Abstract

This article determines an optimal forestry contract when firms’ harvesting costs are interdependent. The value of the optimal allocation depends on the private signals of all firms. We show that the optimal rotation of the winning firm must satisfy a modified version of the usual Faustmann rule, which holds under perfect information. This modification is necessary in order to induce the revelation of private signals on the part of all participating firms. We find conditions under which the optimal mechanism can be implemented as a second-price auction. The optimal rotation period and the reservation price are derived. Theoretically and numerically, we show that the predicted forest owner surplus is considerably misestimated under the independent private value paradigm and the predicted forest owner profit is more affected when the interdependence is negative.

June 8, 2019

B_i and Branching Strict Nash Networks in Two-way Flow Models: A Generalized Sufficient Condition

Banchongsan Charoensook

Article number: 20180117

Abstract

B i and branching networks are two classes of minimal networks often found in the literature of two-way flow Strict Nash networks. Why so? In this paper, we answer this question by establishing a generalized condition that holds together several models in the literature, and then show that this condition is sufficient to guarantee their common result: every non-empty component of minimal Strict Nash network is either a branching or B i network. This paper, therefore, contributes to the literature of two-way flow Strict Nash networks by merging together several existing works.

June 8, 2019

Pay-What-You-Want in Competition

Margaret Samahita

Article number: 20180063

Abstract

This paper presents an analysis of Pay-What-You-Want (PWYW) in competition which explains its entry and limited spread in the market. Sellers choose their pricing schemes sequentially while consumers share their surplus. The profitability and popularity of PWYW depend not only on consumers’ preferences, but also on market structure, product characteristics and sellers’ strategies. While there is no PWYW equilibrium, given a sufficiently high level of surplus-sharing and product differentiation, PWYW is chosen by later entrants to avoid Bertrand competition. The equilibrium results and their market characteristics are consistent with empirical examples of PWYW.

June 11, 2019

Two Rationales for Insufficient Entry

Linfeng Chen, Tan Li, Bing Qian

Article number: 20180054

Abstract

This study offers two new rationales for insufficient entry in a given industry. The first is the presence of complementary industries. Suppose there is free entry in an industry and the complementary industries are monopolistic. If the number of complementary industries is sufficiently high, then there is insufficient entry. However, if these industries are substitutes, then there is always excessive entry. The second rationale is that there is cost-reducing R&D investment and spillover. When the spillover rate is sufficiently high, there is insufficient entry. Further, we consider the general model and obtain similar results.

June 12, 2019

Students’ Social Origins and Targeted Grading

Alessandro Tampieri

Article number: 20170146

Abstract

We study an economy where a school can target grades according to students’social groups, and privileged students are more likely to obtain a high academic achievement. In this context, we analyse the welfare effects of introducing alternative policies. Banning targeted grading generally maximises welfare, through an increase in the wage of privileged students. This result does not hold though when the proportion of high achievers is large, and labour demand is high. In this case, banning wage discrimination among social groups maximises welfare, through an increase in the wages of underprivileged students.

June 18, 2019

Pricing, Signalling, and Sorting with Frictions

Mats Godenhielm, Klaus Kultti, Tuomo Virkola

Article number: 20180108

Abstract

We analyse signalling and sorting in a market with frictions and private information. Buyers are heterogeneous, the sellers choose what quality to produce and post prices. Buyers do not observe quality, but infer it from prices. In equilibrium high-quality sellers signal quality with a price that is higher than under perfect information. Compared to the outcome under perfect information the higher price has two effects. First, it makes production of high-quality goods more attractive increasing its supply. Second, it makes high-valuation buyers worse-off, directing part of them to low-quality sellers. We determine which effect dominates; whether too many or too few sellers produce high quality. We also show that the prices of both high- and low-quality goods are higher, and the sellers do better and the buyers worse under private information. In addition, we show that an increase in the production cost of high quality may lead to higher profits and prices.

June 25, 2019

On the Economic Value of Signals

Adib Bagh, Yoko Kusunose

Article number: 20180191

Abstract

We provide sufficient conditions for the economic value of a signal to be a convex function, either locally or globally, of the input required to produce the signal. We also provide conditions under which this input can be interpreted as a measure of the information contained in this signal. We demonstrate that, under certain conditions, information is a very peculiar good that can—globally—show increasing marginal utility. In contrast to the earlier approach used to obtain the classic results on the local lack of concavity of the value of information, our approach allows permits the investigation of concavity (or lack) of the function representing the value of information, without imposing any conditions of differentiability on this function. Our approach also allows us to show that the marginal value of information can be zero even at an informative signal. Finally, we discuss some of the difficulties that can arise in designing price discrimination schemes for selling signals with various levels of quality.

June 26, 2019

The Core in Bertrand Oligopoly TU-Games with Transferable Technologies

Aymeric Lardon

Article number: 20180197

Abstract

In this article we study Bertrand oligopoly TU-games with transferable technologies under the α and β -approaches. We first prove that the core of any game can be partially characterized by associating a Bertrand oligopoly TU-game derived from the most efficient technology. Such a game turns to be an efficient convex cover of the original one. This result implies that the core is non-empty and contains a subset of payoff vectors with a symmetric geometric structure easy to compute. We also deduce from this result that the equal division solution is a core selector satisfying the coalitional monotonicity property on this set of games. Moreover, although the convexity property does not always hold even for standard Bertrand oligopolies, we show that it is satisfied when the difference between the marginal cost of the most efficient firm and the one of the least efficient firm is not too large.

July 23, 2019

Reasoning About ‘When’ Instead of ‘What’: Collusive Equilibria with Stochastic Timing in Repeated Oligopoly

Justin Grana, James Bono, David Wolpert

Article number: 20180038

Abstract

We analyze a continuous time game of Bertrand competition with private monitoring that includes asynchronous signals and asynchronous actions. Unlike existing models where firms observe a signal that is imperfectly correlated with demand parameters and firms’ prices, we assume firms observe demand and prices perfectly but at times governed by independent Poisson processes. The signals only reveal information at the instant they are observed and do not contain information about past actions or states of demand. This implies that any firm’s price change will go undetected for some time or may never be detected. Firms are also allowed to engage in costless but unverifiable cheap talk. The model focuses on the strategic considerations that arise when firms reason about then timing of the signals rather than the content. We show that standard Nash reversion arguments can enforce collusion and truthful communication when signals are asynchronous and signals only reveal information about the current state of the world and do not reveal information about past states or actions. Through comparative statics, we disentangle how parameters that govern the timing of events and signals interact to either facilitate or preclude collusion. Finally, we extend the model to show that firms may collude not only to avoid Nash reversion but to prevent opposing firms from believing demand has dropped and thus lowering their price.

August 23, 2019

Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims

Hitoshi Matsushima

Article number: 20180088

Abstract

This study investigates strategic aspect of leverage-driven bubbles from the viewpoint of game theory and behavioral finance. Even if a company is unproductive, its stock price grows up according to an exogenous reinforcement pattern. During the bubble, this company raises huge funds by issuing new shares. Multiple arbitrageurs strategically decide whether to ride the bubble by continuing to purchase shares through leveraged finance. We demonstrate two models that are distinguished by whether crash-contingent claim, i. e. contractual agreement such that the purchaser of this claim receives a promised monetary amount if and only if the bubble crashes, is available. We show that the availability of this claim deters the bubble; without crash-contingent claim, the bubble emerges and persists long even if the degree of reinforcement is insufficient. Without crash-contingent claim, high leverage ratio fosters the bubble, while with crash-contingent claim, it rather deters the bubble. We formulate these models as specifications of timing game with irrational types; each player selects a time in a fixed time interval, and the player who selects the earliest time wins the game. We assume that each player is irrational with a small but positive probability. We then prove that there exists the unique Nash equilibrium; according to it, every player never selects the initial time. By regarding arbitrageurs as players, we give careful conceptualizations that are necessary to interpret timing games as models of leverage-driven bubbles.

September 17, 2019

Costly Rewards and Punishments

Frances Z. Xu Lee

Article number: 20180131

Abstract

To punish an agent, the principal often incurs costs. I study a principal’s least costly reward and punishment scheme for an agent whose effort the principal cannot observe. I find the principal’s cost is sometimes minimized by using both costly rewards and costly punishments because (1) the agent has an outside option, or (2) a principal without commitment ability repeatedly interacts with the agent. I also find that when an agent’s effort is better at increasing the probability of a good outcome for the principal, the agent’s payoff may decrease, because the principal replaces rewards with punishments.

September 20, 2019

Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies

Anuj Bhowmik, Maria Gabriella Graziano

Article number: 20180139

Abstract

This paper analyses two properties of the core in a two-period exchange economy under uncertainty: the veto power of arbitrary sized coalitions; and coalitional fairness of core allocations. We study these properties in relation to classical (static) and sequential (dynamic) core notions and apply our results to asset markets and asymmetric information models. We develop a formal setting where consumption sets have no lower bound and impose a series of general restrictions on the first period trades of each agent. All our results are applications of the same lemma about improvements to an allocation that is either non-core or non-coalitionally fair. Roughly speaking, the lemma states that if all the members of a coalition achieve a better allocation in some way (for instance, by blocking the status quo allocation or because they envy the net trade of other coalitions) then an alternative improvement can be obtained through a perturbation of the initial improvement.

Open Access September 20, 2019

Strategic Activism in an Uncertain World

Allard van der Made

Article number: 20180103

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Abstract

We model private politics in the presence of two-sided incomplete information. An interest group (IG) threatens to inform consumers about a firm’s damaging technology should the firm not adopt a clean technology. The IG does not know how costly adopting the clean technology is and the firm does not know how much the IG cares about the damages. In equilibrium an IG who cares a lot signals its type to the firm and the firm is more inclined to adopt the clean technology if it receives such a signal. However, impasses can occur: the firm does not adopt the clean technology despite the fact that the IG has signaled that it cares a lot and threatens to inform a large fraction of the consumer population. The IG never informs all consumers: as soon as a certain fraction of the consumers is informed by the IG the firm reduces its price and thereby reveals to the remaining consumers that it is employing a damaging technology. The IG’s actions increase consumer well-being, but decrease total welfare unless the cost of adopting the clean technology is likely to be low. Yet, since the IG is inclined to target firms with this property, a regulator might want to delegate information provision to the IG.

October 1, 2019

On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy

Ronaldo Carpio, Meixin Guo

Article number: 20180144

Abstract

We introduce a novel method of proving existence of rational expectations equilibria (REE) in multi-dimensional CARA-Gaussian environments. Our approach is to construct a mapping from agents’ initial beliefs (which are characterized by a positive semidefinite matrix), to their updated beliefs, after reaching and observing equilibrium; we then show Brouwer’s fixed point theorem applies. We apply our approach to a finite-market version of Admati (1985), which is a multi-asset noisy REE asset pricing model with dispersed information. We present an algorithm to numerically solve for equilibrium of the finite model, as well as several examples illustrating the difference in equilibrium behavior between the finite and infinite models. Our method can be applied to any multi-dimensional REE model with Gaussian uncertainty and behavior that is linear in agents’ information.

October 11, 2019

Optimal Incentives Under Gift Exchange

Hayat Khan

Article number: 20180041

Abstract

This paper studies optimal incentives in the presence of an agent’s preference for generosity, where the principal optimally chooses the level of generosity (rent) as well as the performance-based pay. We show that some minimum level of reciprocity is required for generous contracts to become attractive. More reciprocal agents exert greater effort, but they may not necessarily receive more generous offers, as our model predicts a hump-shaped relationship between generosity and the reciprocity parameter. This means that moderately reciprocal agents tend to receive a premium relative to weakly or strongly reciprocal agents. Generosity and performance-based pay are likely to behave as complements when risk-sharing motives (determined by noise in the environment and the agent’s degree of risk-aversion) are strong, and they are likely to behave as substitutes when risk-sharing motives are relatively moderate. Moreover, base-wage gifts are always optimal, whereas piece-rate or composite gifts are only optimal in a low-noise environment.

October 8, 2019

Public Good Indices for Games with Several Levels of Approval

Sébastien Courtin, Bertrand Tchantcho

Article number: 20190068

Abstract

This work focuses on ( j , 2) games in which there are several levels of approval in the input, i. e . games with n players, j ordered qualitative alternatives in the input level and 2 possible ordered quantitative alternatives in the output. When considering ( j , 2) games, we extend the Public Good index ( PGI ), the Null Player Free index ( NPFI ) and the Shift index ( SI ) and provide full characterizations of these extensions.

October 22, 2019

Vagueness of Language: Indeterminacy under Two-Dimensional State-Uncertainty

Saori Chiba

Article number: 20180093

Abstract

We study indeterminacy of indicative meanings (disagreements about meanings of messages among players), a kind of language vagueness examined in Blume and Board (2013. “Language Barriers.” Econometrica 81 (2): 781–812). They, using a cheap talk model in which the state-distribution and the players’ language competence were ex-ante uncertain, demonstrated that this vagueness occurs as an equilibrium language. We expand the work of Blume and Board by using a model between an uninformed decision maker and an informed agent in which the state-distribution and the state are both ex-ante uncertain. We show that this two-dimensional uncertainty also leads to indeterminacy of indicative meanings, that is, to a set of conditions in which an agent with different perceptions of the state-distribution intentionally uses the same symbol for the different extents of information on the state. The vagueness, contrary to common expectations, can actually lead to welfare improvement.

October 22, 2019

Winners and Losers of Universal Health Insurance: A Macroeconomic Analysis

Wung Lik Ng, Yin-Chi Wang

Article number: 20180064

Abstract

This paper studies the supply-side distortions and the consequences resulted from provider-side cost containing universal health insurance (UHI) scheme. A two-sector overlapping generations model of endogenous physicians’ specialty choice is presented. We find that the general public is possible to be benefited from the cost containing UHI if the quality of medical services does not deteriorate too much. However, physicians in the medical service sector suffer from such scheme and end up earning lower incomes, regardless of one’s specialty and talent. Inequality among physicians also increases.

November 20, 2019

Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy

Hitoshi Matsushima

Article number: 20190030

Abstract

This study investigates infinitely repeated games of a prisoner’s dilemma with additive separability in which the monitoring technology is imperfect and private. Behavioral incentives indicate that a player is not only motivated by pure self-interest but also by social preference such as reciprocity, and that a player often becomes naïve and selects an action randomly due to her cognitive limitation and uncertain psychological mood as well as the strategic complexity caused by monitoring imperfection and private observation. By focusing on generous tit-for-tat strategies, we characterize a behavioral version of Nash equilibrium termed behavioral equilibrium in an accuracy-contingent manner. By eliminating the gap between theory and evidence, we show that not pure self-interest but reciprocity plays a substantial role in motivating a player to make decisions in a sophisticated manner.

November 20, 2019

Flourishing as Productive Tension: Theory and Model

Aviad Heifetz, Enrico Minelli

Article number: 20180162

Abstract

Based on insights from psychology, we argue that individual well-being has two incommensurable dimensions, gratification and flourishing. We provide a model in which the individual’s vitality is tunneled to different goals/practices. Gratification is represented by discharge of flow, while flourishing corresponds to generated power. The two dimensions are correlated in a way that depends on the characteristics of the available goals/practices, and their relationship need not be monotonic. We also extend the model to social interaction, prove existence of an equilibrium and show the possibility of ‘flourishing traps’.

Notes

June 8, 2019

A Note on Reference-Dependent Choice with Threshold Representation

Dan Qin

Article number: 20180142

Abstract

This note considers reference-dependent choice procedures shaped by a utility function and a threshold function. Alternatives are considered only when the utility gain of moving from the reference is bigger than the threshold. We impose no requirement on the threshold functions whereas previous works characterize the special case of strictly positive threshold functions. We also examine the case when the threshold function depends on both compared alternatives.

June 12, 2019

Regular Equilibria and Negative Welfare Implications in Delegation Games

Tomoya Tajika

Article number: 20180056

Abstract

This study examines delegation games in which each player commits to a reaction function in advance. We focus on the regular subgame perfect equilibria of delegation games in the sense that the chosen reaction functions have an invertible Jacobian. Subsequently we provide a necessary condition under which an action profile is achieved as a regular equilibrium of n -player delegation games. In two-player games with misaligned preferences, each efficient action profile violates the necessary condition. We also show that almost action profiles other than efficient ones are achieved as regular equilibria of the delegation game in which the chosen reaction functions are linear. This finding implies that each delegatee’s objective is written as a quadratic function, which may justify the linear-quadratic specification of the objective functions in applications.

June 12, 2019

Unbundling Production with Decreasing Average Costs

Oriol Carbonell-Nicolau

Article number: 20180097

Abstract

This paper argues that, even in the presence of decreasing average costs of production, monopolies can sometimes be avoided in the interest of market efficiency. It is shown that under certain conditions on the variable cost of production, there is an alternate, viable market structure that reduces the well-known deadweight loss of monopoly: an “upstream” market in which one or more firms own and share the fixed cost of creating and maintaining a distribution network, and a “downstream” market populated by a large number of firms that are charged a unit price for the network’s usage.

September 12, 2019

A Simple and Procedurally Fair Game Form for Nash Implementation of the No-Envy Solution

Makoto Hagiwara

Article number: 20190051

Abstract

We consider the allocation problem of infinitely divisible resources with at least three agents. For this problem, Thomson ( Games and Economic Behavior , 52: 186-200, 2005) and Doğan ( Games and Economic Behavior , 98: 165-171, 2016) propose “simple” but not “procedurally fair” game forms which implement the “no-envy” solution in Nash equilibria. By contrast, Galbiati ( Economics Letters , 100: 72-75, 2008) constructs a procedurally fair but not simple game form which implements the no-envy solution in Nash equilibria. In this paper, we design a both simple and procedurally fair game form which implements the no-envy solution in Nash equilibria.

September 1, 2019

Decision Making and Games with Vector Outcomes

Jaeok Park

Article number: 20180170

Abstract

In this paper, we study decision making and games with vector outcomes. We provide a general framework where outcomes lie in a real topological vector space and the decision maker’s preferences over outcomes are described by a preference cone, which is defined as a convex cone satisfying a continuity axiom. Further, we define a notion of utility representation and introduce a duality between outcomes and utilities. We provide conditions under which a preference cone is represented by a utility and is the dual of a set of utilities. We formulate a decision-making problem with vector outcomes and study optimal choices. We also consider games with vector outcomes and characterize the set of equilibria. Lastly, we discuss the problem of equilibrium selection based on our characterization.

November 15, 2019

Capital Concentration and Wage Inequality

Jiancai Pi, Yanwei Fan

Article number: 20190049

Abstract

This paper analyzes how capital concentration affects wage inequality through the channel of financial frictions. Higher capital concentration can be regarded as the Piketty effect. Under the framework of cost constrained financial frictions, we find that higher capital concentration will expand (resp. narrow down) wage inequality if the asset-liability ratio in the skilled sector is high (resp. low) enough relative to that in the unskilled sector.

November 28, 2019

Annuity Markets and Capital Accumulation

Shantanu Bagchi, James A. Feigenbaum

Article number: 20180055

Abstract

We examine how the absence of annuities in financial markets affects capital accumulation in a two-period overlapping generations model. Our findings indicate that the effect on capital is ambiguous in general equilibrium, because there are two competing mechanisms at work. On the one hand, the absence of annuities increases the price of old-age consumption relative to the price of early-life consumption. This induces a substitution effect that reduces saving and capital, and an income effect that has the opposite effect as households want to consume less when young, causing them to save more. On the other hand, accidental bequests originate from the assets of the deceased under missing annuity markets. The bequest received in early life always has a positive income effect on saving, but the bequest received in old age, conditional on survival, is effectively a partial annuity with both substitution and income effects. We find that when the desire to smooth consumption is high, the income effects dominate, so the capital stock always increases when annuity markets are missing. However, when the desire to smooth consumption is low, the substitution effects dominate, and the capital stock decreases with missing annuity markets.

About this journal

Objective
The B.E. Journal of Theoretical Economics (BEJTE) welcomes submissions in all areas of economic theory, both applied and pure theory, as well as submissions on economic experiments that feature substantial theory components. The journal especially welcomes novel approaches and interdisciplinary work on economic theory. The editors of the BEJTE understand that novel and interdisciplinary approaches may be difficult to evaluate, that their relationship to standard approaches may not be entirely clear yet, and that not all potential applications of such novel and interdisciplinary have been fully developed yet. Pure theory papers to be published in the BEJTE include, but are by no means limited to, those in behavioral economics, decision theory, game theory, general equilibrium theory, information economics, mechanism design, matching theory, networks, and entirely new fields yet to be created. Applications could encompass, but are not restricted to, contract theory, financial economics, industrial organization, internet economics, labor economics, law and economics, personnel economics, public finance, and novel applications yet to be developed.

Topics

behavioral economics
decision theory
game theory
general equilibrium theory
information economics
mechanism design
contract theory
matching theory
social networks

Article formats
BEJTE recently switched from the previous four-tier system (Frontiers, Advances, Contributions, and Topics) to a two-tier system. Besides "Research Articles" we publish now also "Notes", which typically are more concise manuscripts.

> Information on submission process

Volume 20 Issue 1 -

Issue of The B.E. Journal of Theoretical Economics

Optimal Forestry Contract with Interdependent Costs

Abstract

Bi and Branching Strict Nash Networks in Two-way Flow Models: A Generalized Sufficient Condition

Abstract

Pay-What-You-Want in Competition

Abstract

Two Rationales for Insufficient Entry

Abstract

Students’ Social Origins and Targeted Grading

Abstract

Pricing, Signalling, and Sorting with Frictions

Abstract

On the Economic Value of Signals

Abstract

The Core in Bertrand Oligopoly TU-Games with Transferable Technologies

Abstract

Reasoning About ‘When’ Instead of ‘What’: Collusive Equilibria with Stochastic Timing in Repeated Oligopoly

Abstract

Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims

Abstract

Costly Rewards and Punishments

Abstract

Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies

Abstract

Strategic Activism in an Uncertain World

Abstract

On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy

Abstract

Optimal Incentives Under Gift Exchange

Abstract

Public Good Indices for Games with Several Levels of Approval

Abstract

Vagueness of Language: Indeterminacy under Two-Dimensional State-Uncertainty

Abstract

Winners and Losers of Universal Health Insurance: A Macroeconomic Analysis

Abstract

Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy

Abstract

Flourishing as Productive Tension: Theory and Model

Abstract

A Note on Reference-Dependent Choice with Threshold Representation

Abstract

Regular Equilibria and Negative Welfare Implications in Delegation Games

Abstract

Unbundling Production with Decreasing Average Costs

Abstract

A Simple and Procedurally Fair Game Form for Nash Implementation of the No-Envy Solution

Abstract

Decision Making and Games with Vector Outcomes

Abstract

Capital Concentration and Wage Inequality

Abstract

Annuity Markets and Capital Accumulation

Abstract

B_i and Branching Strict Nash Networks in Two-way Flow Models: A Generalized Sufficient Condition