Efficiency is analyzed in a Walrasian model of labor markets with adverse selection. Workers are distinguished by productivity and preferences; firms are distinguished by productivity and ability to distinguish workers. An equilibrium is defined to be constrained efficient if it cannot be dominated by an incomplete mechanism. The set of equilibria turns out to have an interesting structure. Within the class of strongly monotonic economies, there exists at least one efficient equilibrium. Under slightly stronger conditions, an equilibrium is dominated by an incomplete mechanism only if it can be dominated by another equilibrium, that is, equilibria are Pareto optimal. Copyright 1991 by The Review of Economic Studies Limited.

The competitive or Walrasian equilibrium has a well-known stability property-every Walras allocation belongs to the core of the economy. In an earlier paper (Gale, 1978) analogous results were shown to hold in a sequence economy with money. One of the limitations of that paper was the assumption of a complete set of securities. The extension of these results to an economy with only one asset (money) and several states of nature turns out to be frought with difficulty. The equilibrium in this case is highly unstable. Unless some quite unacceptable restrictions are imposed, there will always exist a group of consumers who can make themselves better off than they would be in equilibrium. The intractability of the problem casts doubt on the whole Edgeworthian programme of modelling market equilibrium as the outcome of a cooperative game. Consider a pure exchange economy in which there are two dates, indexed t = 0, 1, but no uncertainty. At each date a single consumption good is available. The economy comprises two consumers, A and B, who have identical tastes but different endowments. Their preferences are described by the utility function u(x) = [x ]2+[x']2 (X E R+) where xt denotes consumption at date t. Their endowments are described by the ordered pairs

of Mannheim University has brought to my attention an error in my paper "Large Economies with Trading Uncertainty". The example of an allocation mechanism described on pp. 329-332 does not satisfy the condition of relative continuity as claimed on p.332. The reason is that the definition, as given in the paper, is a rather gross misstatement of what I had in mind and makes some of the accompanying analysis nonsensical. Fortunately, the matter is not hard to put right. Two passages in the text must be rewritten as follows.

Journal Article Large Economies with Trading Uncertainty Get access Douglas Gale Douglas Gale London School of Economics Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 46, Issue 2, April 1979, Pages 319–338, https://doi.org/10.2307/2297055 Published: 01 April 1979 Article history Received: 01 September 1975 Accepted: 01 April 1978 Published: 01 April 1979

The paper studies a market in which there are two sellers and one buyer. Each agent wants to trade at most one unit of an indivisible commodity. The sellers are uncertain whether the buyer is receiving offers from one or both of them at any given time. This model induces competitive and monopolistic outcomes for particular parameter values. But, other things being equal, as the buyer becomes very patient, the equilibrium price converges to the competitive one.

[A model of decentralized exchange and price formation is defined using the bargaining theory of A. Rubinstein. Agents meet at random and bargain over the terms of trade. If there are no transaction costs, every perfect equilibrium of the bargaining game implements a Walrasian equilibrium of the underlying exchange economy.]

Extensive-form market games typically have a large number of noncompetitive equilibria. In this paper, we argue that the complexity of noncompetitive behavior provides a justification for competitive equilibrium in the sense that if rational agents have an aversion to complexity (at the margin), then maximizing behavior will result in simple behavioral rules and hence in a competitive outcome. For this purpose, we use a class of extensive-form dynamic matching and bargaining games with a finite number of agents. In particular, we consider markets with heterogeneous buyers and sellers and deterministic, exogenous, sequential matching rules, although the results can be extended to other matching processes. If the complexity costs of implementing strategies enter players’ preferences lexicographically with the standard payoff, then every equilibrium strategy profile induces a competitive outcome.

The authors characterize the symmetric equilibria of an investment game with a pure informational externality. When the period length is very short, the game ends very quickly; with positive probability, an informational cascade (herding) causes an investment collapse. As the period length increases, the possibility of herding disappears. As the number of players increases, the rate of investment and the information flow are eventually independent of the number of players; adding more players simply increases the number who delay. In the limit, a period of low investment is followed by either an investment surge or a collapse. Copyright 1994 by The Econometric Society.