For an arbitrary data set D = {(p, x)} ⊆ (ℝ+m∖ {0}) × ℝ+m, finite or infinite, it is shown that the following three conditions are equivalent: (a) D satisfies GARP; (b) D can be rationalized by a utility function; (c) D can be rationalized by a utility function that is quasiconcave, nondecreasing, and that strictly increases when all its coordinates strictly increase. Examples of infinite data sets satisfying GARP are provided for which every utility rationalization fails to be lower semicontinuous, upper semicontinuous, or concave. Thus condition (c) cannot be substantively improved upon.

We generalize Athey's (2001) and McAdams' (2003) results on the existence of monotone pure-strategy equilibria in Bayesian games. We allow action spaces to be compact locally complete metric semilattices and type spaces to be partially ordered probability spaces. Our proof is based on contractibility rather than convexity of best-reply sets. Several examples illustrate the scope of the result, including new applications to multi-unit auctions with risk-averse bidders.

A game is better-reply secure if for every nonequilibrium strategy x* and every payoff vector limit u* resulting from strategies approaching x*, some player i has a strategy yielding a payoff strictly above ui* even if the others deviate slightly from x*. If strategy spaces are compact and convex, payoffs are quasiconcave in the owner's strategy, and the game is better-reply secure, then a pure strategy Nash equilibrium exists. Better-reply security holds in many economic games. It also permits new results on the existence of symmetric and mixed strategy Nash equilibria.

A weakening of D. Kreps and R. Wilson's (1982) notion of sequential rationality is presented. The motivation stems from the difficulty in justifying sequentially rational behavior in subgames reachable only through a violation of sequential rationality. Although the present notion of weak sequential rationality is based upon extensive form considerations, it bears a close relation to R. Selten's (1975) normal form perfect equilibria. Backward induction outcomes can be achieved in generic games of perfect information with additional restrictions on beliefs. An example with imperfect information shows that sequential rationality is not the consequence of equilibrium play and the absence of incredible threats.

Stable matchings in school choice needn’t be Pareto efficient and can leave thousands of students worse off than necessary. Call a matching μ priority-neutral if no matching can make any student whose priority is violated by μ better off without violating the priority of some student who is made worse off. Call a matching priority-efficient if it is priority-neutral and Pareto efficient. We show that there is a unique priority-efficient matching and that it dominates every priority-neutral matching and every stable matching. Moreover, truth-telling is a maxmin optimal strategy for every student in the mechanism that selects the priority-efficient matching.

We establish the existence of pure strategy equilibria in monotone bidding functions in first-price auctions with asymmetric bidders, interdependent values, and affiliated one-dimensional signals. By extending a monotonicity result due to Milgrom and Weber (1982), we show that single crossing can fail only when ties occur at winning bids or when bids are individually irrational. We avoid these problems by considering limits of ever finer finite bid sets such that no two bidders have a common serious bid, and by recalling that single crossing is needed only at individually rational bids. Two examples suggest that our results cannot be extended to multidimensional signals or to second-price auctions. Copyright The Econometric Society 2004.

We provide an ascending auction that yields an efficient outcome when there are many identical units for sale and bidders have interdependent values and downward-sloping demand. Our ascending auction both extends and generalizes Ausubel's (2004) and yields the same outcome as Perry and Reny's (2002) generalization of Vickrey's (1961) sealed-bid auction. There are two key features of our auction. Bidders are permitted both to express different demands against different bidders, as well as to increase their demands. The equilibrium strategies are closely related to the familiar “drop out when price equals value” strategy of the English auction.

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 a ¢ liated private information. If there are su ¢ ciently many buyers and sellers, and their bids are restricted to a su ¢ ciently …ne 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 e ¢ cient and almost fully aggregates the agents’information. 1.