## 1 Introduction

Firms improve their production technology through a variety of means, many of which are unobservable to the outside world. This is, in particular, true for a very significant proportion of innovations and other production efficiency gains that arise through learning, internal research and development (R&D), and accumulation of organizational capital. As many of these gains are not patentable, firms prefer to retain privacy of information about their actual cost and technology structure. More interestingly, it is difficult for existing rivals, potential competitors, and other stakeholders in the industry to readily acquire information about efforts and inputs expended in the R&D process of a firm. In competitive markets, the absence of observability of R&D investment or efforts undertaken by other firms is likely to influence the strategic incentive to invest, the extent of actual technological improvements, and the eventual market outcomes. This leads to an important question about the effect of privacy of such information on technological change and social welfare. If such secrecy is not socially desirable, then there would be a case for public policy to discourage secrecy and promote sharing and disclosure of information about R&D investments made by the firms. This paper attempts to analyze the potential impact of secrecy of the level of R&D investment made by the firms in a market characterized by privacy of information about the actual cost structure of the firms i. e., their actual production technology.

My paper draws on the seminal work of Gal-or (1986) who finds that firms strategically competing in prices do not have any incentive to disclose information about their own cost of production. In this paper, I assume that firms keep their final outcome of process innovation secret and primarily focus on the role of (exogenously given) secrecy of strategic R&D investment. Moreover, in contrast to this paper, the existing literature has largely focused on issues related to the observability of cost or R&D outcomes. Thomas (1997) examines the incentive for cost-reduction by a single firm in an industry where firms differ in their initial cost and shows that this unilateral incentive for cost-reduction is higher when information about actual production cost is privately held.

In particular, the paper analyzes an *ex ante* symmetric homogenous good duopoly where firms engage in process innovation (that reduces production cost) and price competition. The firms simultaneously decide whether to invest in cost-reduction and after this, they compete in prices. The realized cost-reduction is uncertain and depends on the amount of investment. Each firm observes its own realized production cost outcome prior to price setting but remains unaware of the actual outcome of the R&D investment made by its rival. I compare the incentive to invest in cost-reduction and the market outcome generated in this extensive form with the secrecy of investment to the equilibrium outcome of an alternative extensive form where the level of R&D investment is publicly observed before price setting. The realized cost i. e., the outcome of R&D is assumed to be private information in both extensive forms.

The main result of the paper is the equilibrium outcome under secrecy of R&D investments yields higher social welfare than public observability of (or information sharing about) investment. Further, secrecy may yield higher total amount R&D investment and higher expected profit for firms.

One implication of this is that there may not be any case for public policy to encourage information sharing arrangements among competing forms about R&D investments. Further, there is some benefit from the protection of information about expenditures, inputs or efforts going into firms’ R&D processes through trade secret laws
^{1} and deterrence of competitive intelligence gathering activities
^{2} related to R&D investment or inputs.

The paper is organized as follows. Section 2 describes the model. In Section 3, I discuss the pricing and investment outcomes under incomplete information when R&D investment is secret and when it is publicly observable.

## 2 The Model

I consider an oligopolistic market with two *ex ante* identical firms that compete in prices and produce a physically homogenous product. The production technology of each firm can be of two potential types: high-cost (*H*) and low-cost (*L*): Each firm produces at constant unit cost. The unit production cost of a high-cost type (defined by *c _{H}*) is greater than that of a low-cost type (defined by

*c*) i. e.,

_{L}*V*for a unit produced by either firm. I assume that

Firms are initially endowed with high-cost technology i. e., each firm incurs a unit production cost of *c _{H}*. Firms can invest in R&D of a new cost-reducing technology. However, the outcome of the investment is uncertain, and the probability of success is positively related to the cost of investment. The cost of investment is given by

*A*, can be interpreted as the maximum possible cost of investment that a firm can incur and

^{3}.

In the first stage, the firms simultaneously decide how much to invest (viz., ^{4}. It is evident that the more a firm invests in cost-reducing technological R&D, the higher is the probability of being successful i. e., becoming a low-cost type firm. I consider two possible scenarios after the firms decide on their R&D investment in the first stage. (1) The investment decisions become publicly observable but the firms remain unaware of the final outcome of the investment made by the rival firms; in the rest of the paper, I refer to this as the “*incomplete information with observable investment*”. The alternative scenario is where (2) the investment decision of each firm remains private knowledge (secret) and thus, a firm neither observes the rival’s investment decision nor the final outcome of the rival’s investment; this is referred as the “incomplete information with unobservable investment”. I denote the investment outcomes and the *ex ante* expected profits under incomplete information with observable investment as well as with unobservable investment with superscript *IO* and *IU* respectively. The realizations of the production technology after investment are independent across firms, and there is no spill over. In the next stage, firms choose prices simultaneously. Finally consumers observe the prices charged by the firms, decide whether to buy, and from which firm to buy.

## 3 Observability vs Secrecy

After the strategic investment decisions in the first stage, a firm gets to know the actual outcome of its own investment in the cost-reduction, but does not learn anything about the rival’s R&D outcome. Therefore, when the firms simultaneously choose price of their product they are not aware of each other’s marginal cost of production i. e., a firm does not know whether the rival has successfully adopted the low-cost technology.

To begin with, I solve the second stage (incomplete information) subgame where firms choose prices simultaneously with the private knowledge of their own production technology
^{5}. Without any loss of generality, I assume that *i* is more likely to successfully install the new low-cost technology than firm.

*The high-cost type charges a price equal to its own unit production cost**and the low-cost type randomizes over an interval**with probability distributions*

*where*

*and*

*The ex ante expected profits are*

First, note that there does not exist any Bayesian price equilibrium in pure strategies. The reason is as follows. The low-cost type has competitive advantage over the high-cost type since *i* has a mass point on the upper bound; in other words, firm *i* has higher probability of charging the upper bound (*c _{H}*) of the price distribution than firm

*j*does. Further, firm

*i*of low-cost type charges the upper bound (

*c*) when it believes that the rival

_{H}*j*has remained a high-cost type with probability

*i*is

*j*earns the same profit

^{6}on the upper bound (

*c*) for firm

_{H}*j*. Also, if

At any price *i* is

*j*remains high-cost type and

*j*has become low-cost type but it does not undercut the firm

*i*i. e., does not charge a price below

*p*; similarly, the profit of the low-cost type of firm

*j*is

*i*and firm

*j*as

A firm earns a strictly positive expected profit because of its strictly positive investment. Moreover, the expected profit of the firm with higher investment depends on the probability of failure of the rival with lower investment, but not the vice versa; because the low-cost type of the firm with higher as well as lower investment earn the same expected profit over the (same) price interval. Note that the Bayesian pricing equilibrium is the same irrespective of the observability of the firms’ strategic investment decisions.

First, I consider the case where the strategic investment decisions become **observable**. In the first stage, firm *i* chooses *j* has chosen

*Under incomplete information with**observable**investment, firms choose**and**where**in the Bayesian Nash investment equilibrium*.

I evaluate the best response function of each firm (i. e., given *i* can make) and then find the Nash equilibrium of the investment game. Suppose arg

Observe that for any *ex ante* expected profit of firm *ex ante* expected profit function of firm *i* is given by the second part of eq. [2] i. e.,

*i*for any given

*i*in eqs [4] and [6]. Note that

*i*is

*i*is

*i*under incomplete information with observable investment is given by

*where*

^{7}Bayesian Nash equilibria of the investment game under incomplete information with observable investment are

*ex ante*expected profits for firm

*i*and firm

*j*

■

Figure 1 depicts the reaction functions of the firms (denoted by eq. [7]). In the asymmetric Bayesian Nash equilibria (represented by *E*_{1} and *E*_{2}), one of the firms chooses investment such that it becomes low-type with probability one *A*). Whereas the other firm invests less, remains high-cost type with a strictly positive probability, and earns less profit. Both firms make strictly positive investment to generate uncertainty about the cost structure and thus, in turn, earn strictly positive expected profit. Further, increase in cost differential

Finally, I study the equilibrium investment behavior when the investment in cost-reducing technology remains private knowledge. In other words, a firm knows its own type but is unaware of both the investment and the actual outcome of the rival. Note that in this multistage imperfect information game, the nature of pricing equilibrium outcomes is similar to that of the incomplete information one discussed in Lemma 1.

*Under incomplete information with**unobservable**investment, firms choose**where**in the Bayesian Nash investment equilibrium*.

Suppose *i* deviates to *j* does not observe this deviation and believes that firm *i* has chosen *i* randomizes over a price interval *ex ante* expected profit of firm *i* i. e.,

The expected profit from deviation is maximized at

*j*and the value of

*ex ante*expected profit of each firm is

*j*deviates i. e.,

From the above propositions, one can make the following observations:

- (1)When the investment decisions remain secret, both firms engage is symmetric investment behavior in the equilibrium unlike the case where investment is observable i. e.,
where${\mathrm{\mu}}_{j}^{IO}=\frac{1}{2}(1-\frac{A}{({c}_{H}-{c}_{L})})\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\le {\mathrm{\mu}}_{i}^{IU}={\mathrm{\mu}}_{j}^{IU}=(1-\frac{A}{({c}_{H}-{c}_{L})})\le {\mathrm{\mu}}_{i}^{IO}=1\mathrm{\forall}i,\phantom{\rule{thinmathspace}{0ex}}j=1,\phantom{\rule{thinmathspace}{0ex}}2$ .$i\ne j$ - (2)The
*ex ante*expected profit earned by each firm under secrecy is higher than that of under observable investment i. e.,${\mathrm{\pi}}_{i}^{IU}\ge {\mathrm{\pi}}_{i}^{IO}\phantom{\rule{thinmathspace}{0ex}}\mathrm{\forall}i=1,\phantom{\rule{thinmathspace}{0ex}}2\phantom{\rule{thinmathspace}{0ex}}\mathrm{i}\mathrm{f}\phantom{\rule{thinmathspace}{0ex}}\frac{({c}_{H}-{c}_{L})}{2}\le A<({c}_{H}-{c}_{L})$ - (3)The aggregate (or industry level) investment in R&D under secrecy is higher compared to no secrecy (about the investment behavior) when
$\frac{({c}_{H}-{c}_{L})}{3}\le A<({c}_{H}-{c}_{L}).$ - (4)The aggregate (or industry level)
*ex ante*expected profit under secrecy is higher$\frac{3({c}_{H}-{c}_{L})}{7}\le A<({c}_{H}-{c}_{L}).$ - (5)Social surplus is maximized when a firm charges its own marginal cost. Thus, the expected total surplus is equal to

which is maximized at

## 4 Conclusion

I find that the *ex ante* total expected profit of the industry as well as the social welfare are higher when strategically competing firms keep their R&D investments in cost-reducing technology secret compared to the case when such information is public observable. This implies that the government intervention to secure disclosure of R&D investments may be counterproductive and the trade secret laws that protect privacy of information related to R&D inputs or investment may be conducive to innovation.

## References

Bagnoli, M., and S. Watts. 2015. “Competitive Intelligence and Disclosure.” RAND Journal of Economics 46:709–29.

Gal-or, E. 1986. “Information Transmission – Cournot and Bertrand Equilibria.” Review of Economic Studies 53:85–92.

Routledge, R. 2010. “Bertrand Competition with Cost Uncertainty.” Economics Letters 107:356–9.

Spulber, D. 1995. “Bertrand Competition When Rivals’ Costs Are Unknown.” Journal of Industrial Economics 43:1–11.

Thomas, C. 1997. “Disincentives for Cost-Reducing Investment.” Economic Letters 57:359–63.

## Footnotes

^{1}

In the US, state governments choose to adopt conveniently modified versions of the Uniform Trade Secret Acts (1979).

^{2}

See Bagnoli and Watts (2015) among others.

^{3}

If

^{4}

Alternatively, one can think that the firms choose the probability of successful investment in cost-reducing technology i. e.,

^{5}

Spulber (1995) and Routledge (2010) consider Bertrand price competition under asymmetric information about rival’s cost when firms face downward sloping market demand.

^{6}

This essentially means that since firm *j* has a lower probability of being successful in adopting the low-cost technology compared to its rival firm *i*, firm *j* charges the upper bound of the price interval (i. e., *c _{H}*) with zero probability.

^{7}

It is easy to prove why symmetric equilibrium does not exist. Assume that *i* has a strictly positive incentive to deviate to *i* earns higher expected profit if it decides to invest more than its rival.