貝氏庫諾競爭

Bayesian Cournot Competition

本文考慮廠商對競爭對手成本具有不完全訊息的庫諾競爭模型，所使用的均衡概念是貝氏──納許均衡。庫諾競爭所具備的「總合結構」──每一廠商的報酬由其策略選擇以及所有廠商策略選擇之加總所決定──讓我們得以用一個很簡單的方式來定義均衡。本文顯示當我們考慮的是由「替代函數」所決定所有廠商之相同的總合策略，而非單一廠商之最適反應時，納許均衡即是總合替代函數之定點，而我們可以不必受限於對稱賽局或是僅有兩名參賽者之賽局。我們推導惟一均衡存在的充要條件，此分析法並且更便利比較靜態分析的進行，因為貝氏──納許均衡可以在二度空間定義與顯示。

This paper considers a model of Cournot competition where firms have incomplete information about their rivals’ costs. The equilibrium concept we use is that of Bayesian- Nash equilibrium. Based on the recognition of the “aggregative structure” within Cournot competition in which each firm’s payoff is determined by its own strategy choice and the un-weighted sum of all firms’ strategy choices, we are able to characterize the equilibria in a very simple way. We show that when we consider not the best response but the strategy consistent with a Nash equilibrium in which the aggregate strategy of all players take same value (which is given by what we call the replacement function), then Nash equilibria correspond to fixed points of the aggregate replacement function whose properties we can certainly obtain without need for restricting our attention to symmetric games or games in which there are just 2 players. We develop sufficient conditions under which there is a unique equilibrium. The approach facilitates the analysis of comparative statics, since the characterization of Bayesian-Nash equilibria can be shown on a two-dimensional space.