Abstract
Following the evolutionary game-theoretic approach to analyze Conjectural Variations (CV) in oligopolies, a model is developed to derive the Evolutionarily Stable Strategies (ESS) for quantity-setting and price-setting oligopolies with CV, producing heterogeneous goods. It is shown that ESS coincides with the Consistent CV in the oligopoly model. Earlier studies have demonstrated the above result only for duopolies. It is also shown that the market outcome induced by ESS is socially suboptimal if firms produce heterogeneous products, but can be socially optimal if firms produce homogeneous goods. In general, the market outcome approaches the socially optimal outcome, as the number of firms increases to infinity.
Highlights
The theory of Conjectural Variations (CV) has witnessed several important developments since its origins in the industrial organization literature approximately a century ago (Bowley (1924) [1] and Frisch (1933) [2])
The above authors independently derive Evolutionarily Stable Strategies (ESS) for an evolutionary game involving a duopoly. They show that ESS coincides with the consistent CV of the static duopoly game, as defined by Bresnahan (1981) [3]. This coincidence between the outcomes of a game played by rational players and irrational players can be understood intuitively: only those players which maximize their payoff functions taking into consideration the right conjectures about the rival firm’s behavior will be more successful in the market and these conjectures are the ones that remain in an evolutionary game too
We have generalized the above result for general n-firm oligopoly markets and have analyzed the social optimality of ESS in a differentiated goods oligopoly framework, with both quantity competition and price competition
Summary
The theory of Conjectural Variations (CV) has witnessed several important developments since its origins in the industrial organization literature approximately a century ago (Bowley (1924) [1] and Frisch (1933) [2]). They show that ESS coincides with the consistent CV of the static duopoly game, as defined by Bresnahan (1981) [3] This coincidence between the outcomes of a game played by rational players (i.e. the static duopoly game) and irrational players (i.e. the evolutionary game) can be understood intuitively: only those players which maximize their payoff functions taking into consideration the right conjectures about the rival firm’s behavior will be more successful in the market and these conjectures are the ones that remain in an evolutionary game too. The purpose of this paper is two-fold: First, following the evolutionary duopoly model proposed by Muller and Norman (2005) [9], we derive the ESS for quantity-setting and price-setting oligopolies with conjectural variations, producing heterogeneous goods.
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