We analyze demand function competition with a ﬁnite number of agents and private information. We show that the nature of the private information determines the market power of the agents and thus price and volume of equilibrium trade. We establish our results by providing a characterization of the set of all joint distributions over demands and payoﬀ states that can arise in equilibrium under any information structure. In demand function competition, the agents condition their demand on the endogenous information contained in the price. We compare the set of feasible outcomes under demand function to the feasible outcomes under Cournot competition. We ﬁnd that the ﬁrst and second moments of the equilibrium distribution respond very diﬀerently to the private information of the agents under these two market structures. The ﬁrst moment of the equilibrium demand, the average demand, is more sensitive to the nature of the private information in demand function competition, reflecting the strategic impact of private information. By contrast, the second moments are less sensitive to the private information, reflecting the common conditioning on the price among the agents.
Bergemann, Dirk; Heumann, Tibor; and Morris, Stephen, "Information and Market Power" (2015). Cowles Foundation Discussion Papers. 2454.