Mathematical Social Sciences 37 1999 165–188
Duopoly experimentation: Cournot competition
M. Dolores Alepuz, Amparo Urbano
` Department of Economic Analysis
, University of Valencia, Campus dels Tarongers, Avda. Dels Tarongers, Valencia
, E-46022, Spain Received 26 March 1996; received in revised form 28 February 1998; accepted 19 May 1998
Abstract
This paper analyzes learning behavior in an industry facing uncertainty. We consider a duopoly game where firms have imperfect information about market demand and they learn through
observing market prices. The main body of our study consists of showing how firms make the price a more informative signal through their experimental behavior, and how this behavior
compares to its monopoly counterpart. We extend previous analysis to the case where the demand unknown parameter takes values on the real line. We also find that experimentation under Cournot
duopoly is smaller than under monopoly whenever the demand’s unknown parameter is sufficiently precise.
1999 Elsevier Science B.V. All rights reserved.
Keywords : Experimentation; Duopoly learning
JEL classification : C72; D83
1. Introduction
Firms acting under uncertainty may find it profitable to acquire relevant information. One way to acquire information about an uncertain parameter is via experimentation.
Experimentation by a firm is the use of present actions to vary the amount of information available in the future. However, when these actions are observed by other
firms they also affect their inferences about the same parameter and hence the underlying market competition. It is the purpose of this paper to study experimentation
under competition. This is an extension of Mirman et al., 1993a who study monopoly experimentation, avoiding the competition effect.
We deal with duopoly thus introducing competition and we also consider a continuum of possible values for the slope of demand. Strategic interaction adds a new effect into
Corresponding author. Tel.: 134 6 3828246; fax: 134 6 3828249; e-mail: amparo.urbanouv.es 0165-4896 99 – see front matter
1999 Elsevier Science B.V. All rights reserved.
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. Dolores Alepuz, A. Urbano Mathematical Social Sciences 37 1999 165 –188
the analysis since the result of the experimenting behavior by one firm is observed by the rival. In such a setting and if information is valuable, is there any unilateral incentive
to experiment? Does a monopoly experiment more or less than a duopoly? To answer these questions we propose a two period horizon model played by two
firms. They face a linear inverse demand with a random slope. Each period price is determined by the total quantities together with a random noise. The mean of the random
slope is an unknown parameter and firms have the same subjective probability about it. They cannot precisely infer the true value of this parameter from the market price since
it includes a random noise. The game proceeds as follows: in the first period firms choose simultaneously and independently production levels. These actions together with
the noise term determine the market price. It is assumed that both the market price and the industry output are observable by the firms. In the second period, they again choose
quantities based upon their updated beliefs about the unknown parameter. The expected payoffs of the firms are their two period profits.
By experimenting a firm increases the informational content of its market observa- tions, i.e. prices. However, in order to do that it must give up present period profits. In a
duopoly setting firms affect the informativeness of the commonly observed signal. Thus
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they may affect the degree to which a rival is likely to update. Since firms face a strategic informational choice, an important determinant of their behavior is whether
expected future profits increase with an increase in information. It is well known that, in contrast to a single agent problem, an increase in information in a game may make some
players worse off. We demonstrate that this cannot happen in models like ours, where the demand structure is linear and the a priori information is common.
The main contribution of this article is twofold. First, we generalize duopoly experimentation to the case of a continuum of possible demand curves. We prove that the
informativeness of the commonly observed signal increases with a firm’s output. Second, we relate experimentation and market competition. We find out that what is
relevant is the a priori uncertainty about the random demand. In particular, we show that if the random slope is sufficiently precise which, in turn, makes the commonly observed
market signal precise as well, then the monopoly will experiment more than the Cournotian duopoly. The intuition behind this result can be understood by noting that,
under duopoly, firms face a strategic informational choice in the sense of how informative to make the publicly observed market signal. If initial beliefs about the
random slope are precise so is the market signal and then, posterior beliefs may became
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Related to our work are the ‘signal-jamming’ models of Riordan, 1985; Fudenberg and Tirole, 1986; Mirman et al., 1993b. In these models no firm is perfectly informed about the state of nature and each firm may have
an incentive to manipulate the inferences drawn by rival firms. The principal difference between these signal-jamming models and ours lies in the assumption made about the observability of actions: in
signal-jamming, firms do not know – even ex-post – the action chosen by rivals. Therefore, firms attempt to influence the direction in which a rival updates its beliefs. Urbano, 1993 investigates a model with both
experimentation and signal-jamming under duopoly.
M . Dolores Alepuz, A. Urbano Mathematical Social Sciences 37 1999 165 –188
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too accurate by experimentation. Hence, the rival will be better informed and a tougher competitor: too precise signals discourage experimentation by duopolists.
The value of information in oligopoly games has been the subject of intensive research. These studies typically assume either that firms transmit information through
‘certifiable verifiable announcements’ or that the signals that yield information to the
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firms are exogenously generated. In contrast with them, our model endogenously determines the amount of information available to firms. The closest model to ours is the
duopoly experimentation model of Mirman et al., 1994, who have also generalized the results of Mirman et al., 1993a. Their main contribution is to extend duopoly
experimental behavior to mixed strategy equilibrium and to show some cases for which the net value of information for the duopoly is positive. However, they are unable to
relate the duopoly experimental behavior with that of the monopoly in their general setting. Related to our model but with a different purpose are Aghion et al., 1993;
Alepuz and Urbano, 1993; Harrington, 1995. They assume that the degree of substitution between products is unknown to explain the phenomenon of price dispersion under
oligopoly. Finally, Alepuz and Urbano, 1997 deal with experimental behavior but in asymmetric heterogeneous duopoly markets.
The plan of the paper is as follows. The model and informational assumptions are laid down in Section 2. Then, we analyze the main features of information and the
experimental behavior of firms. Section 3 is devoted to show that larger outputs lead to more informative market signals. Monopoly and duopoly experimentation are compared
in Section 4. Some concluding remarks are given at the end.
2. The Cournot model
