An existence theorem for Cournot–Walras equilibria in a monopolistically competitive economy
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- 作者：Koji Shirai
- 关键词：Monopolistic competition ; General equilibrium with imperfect competition ; Aggregative game ; Potential game ; Additive utility
- 刊名：Journal of Mathematical Economics
- 出版年：2010
- 出版时间：20 November 2010
- 年：2010
- 卷：46
- 期：6
- 页码：1093-1102
- 全文大小：244 K
文摘
We establish an existence theorem for Cournot–Walras equilibria in a monopolistically competitive economy. Instead of the traditional approach which depends on Kakutani’s fixed point theorem, we employ the theories of aggregative games and best reply potential games. We show that, if there exists a representative consumer, under some conditions on preferences and production technologies, the profit maximization game is a (pseudo) best reply potential game. Hence, the existence of the equilibria is proved independently of the well known convex-valued assumption on the best responses. Although our assumptions result in the additive separability on a utility function of a representative consumer, the existence of increasing returns and indivisible productions can be allowed. In our model, it is shown that the game played by firms exhibits strategic substitutes whether the products of firms are substitutes or complements, and this plays an important role for the existence of the equilibria.