Toward a Strategic Foundation for Rational Expectations Equilibrium

Abstract

A step toward a strategic foundation for rational expectations equilibrium is taken by considering a double auction with n buyers and m sellers with interdependent values and affiliated private information. If there are sufficiently many buyers and sellers, and their bids are restricted to a sufficiently fine discrete set of prices, then, generically, there is an equilibrium in nondecreasing bidding functions that is arbitrarily close to the unique fully revealing rational expectations equilibrium of the limit market with unrestricted bids and a continuum of agents. In particular, the large double-auction equilibrium is almost efficient and almost fully aggregates the agents' information. Copyright The Econometric Society 2006.

Information aggregation in a large multi-stage market game

“…Here we show that if the competitive demand for good-q is monotone in L z for each z ∈ Z, and if some mild additional conditions hold, then any equilibrium is fully revealing and can be characterized asymptotically by the unique CE. 13 We split the argument into two parts. We first give sufficient conditions for uniqueness within the class of full-participation equilibria.…”

“…Some of the literature has focused on both efficiency and simplicity under particular mechanisms. Reny and Perry [13] and Vives [17] study double-auction mechanisms and show that those mechanisms achieve ex post efficiency in special settings: Reny and Perry [13] assumes unit demands, while Vives [17] assumes quadratic utilities and normally distributed signals. However, except in such special cases, double auctions are not simple in terms of actions or the way the mechanism uses those actions.…”

“…1 The environment we study is a (static) two-divisible-good, finite number-of-agents, pure-exchange setting in which there is a role for information aggregation. The informationpreference structure is borrowed from Gul and Postlewaite [6] and is closely to related to those in Reny and Perry [13] and Vives [17]. There is an unobserved state-of-the-world, which in our case is drawn from a finite set, and there are private signals, also drawn from a finite set, that are informative about the state.…”

“…3 From the ex ante perspective, it is standard to label any such CE a rational-expectations CE (see, for example, Reny and Perry [13]). From that perspective, our results establish a strategic foundation for rational-expectations CE in a new setting-one with divisible goods, general preferences, a general information structure, and a finite number of agents.…”

“…One is finite supports for the state and for types and the other is the two-good assumption. While a finite number of states may seem more restrictive than the continuum specifications in Reny and Perry [13] and Vives [17], they make strong distributional assumptions that we do not need. Also, our two-good model may seem limited relative to some multiplegood trading-post models.…”