English auctions and the Stolper-Samuelson theorem

We prove that the English auction (with bidders that need not be ex ante identical and may have interdependent valuations) has an efficient ex post equilibrium. We establish this result for environments where it has not been previously obtained. We also prove two versions of the Stolper-Samuelson theorem, one for economies with n goods and n factors, and one for non-square economies. Similar assumptions and methods underlie these seemingly unrelated results.     

Non-marketed options, non-existence of equilibria, and non-linear prices

This paper presents a surprising example that shows that the lattice theoretic properties in Mas-Colell's (1986) seminal work are relevant to the existence of equilibrium even when the commodity space is finite dimensional.The example is a two-period securities model with a three-dimensional portfolio space and two traders. The paper identifies a non-marketed call option that fails to have a minimum cost super-replicating portfolio. Using this option, we construct an economy that satisfies all of Mas-Colell's assumptions, except that the three-dimensional commodity space is not a vector lattice. In this economy, there is no Walrasian equilibrium and the second theorem of welfare economics fails.Our example has important finite- as well as infinite-dimensional implications. It is also an example of a “well behaved” economy in which optimal allocations that are not supported by linear Walrasian prices are decentralized by the non-linear prices studied in Aliprantis-Tourky-Yannelis (2001).     

On the existence of equilibria in economies with infinitely many commodities and without ordered preferences

The present paper deals with the existence of equilibria in economies whose commodity space is L_∞(M, M, μ) and where the agents' preferences need not be complete or transitive. Applying a fixed point theorem of Browder, an equilibrium existence theorem for abstract economies (generalized qualitative games) is proven where each agent's choice set is contained in an arbitrary topological vector space. With the help of this theorem the existence of Walrasian general equilibrium for a suitably specified economic model is obtained. The final result is a generalization of T. F. Bewley's (J. Econ. Theory4 (1972), 514–540) equilibrium existence theorem to the case of non-ordered preferences.     

EFFICIENT MIXED CLUBS: NONLINEAR-PRICING EQUILIBRIA WITH ENTREPRENEURIAL MANAGERS

Scotchmer and Wooders show that efficient clubs are homogeneous when consumers are divisible in Berglas's anonymous crowding model. However, if consumers are not divisible or if clubs have multiple facilities with economies of scope, mixed clubs are efficient. In such a model, we consider clubs with multiple membership policies for different types of consumers, and show the existence and efficiency of equilibrium with nonlinear policies. We employ entrepreneurial equilibrium, all equilibrium concept with profit-seeking entrepreneurs. Our theorem can be regarded as showing the existence of a core allocation that satisfies envy-free property in the absence of non-anonymous crowding effects.     

The efficiency of competitive mechanisms under private information

We consider the efficiency properties of exchange economies where privately informed traders behave strategically. Specifically, a competitive mechanism is any mapping of traders’ reports about their types to an equilibrium price vector and allocation of the reported economy. In our model, some traders may have non-vanishing impact on prices and allocations regardless of the size of the economy. Although truthful reporting by all traders cannot be achieved, we show that, given any desired level of approximation, there is such that any Bayesian-Nash equilibrium of any competitive mechanism of any private information economy with or more traders leads, with high probability, to prices and allocations that are close to a competitive equilibrium of the true economy. In particular, allocations are approximately efficient. A key assumption is that there is small probability that traders behave non-strategically.     

Linear exchange economies with a continuum of agents

The purpose of this paper is to study how the equilibrium prices vary with respect to the initial endowments in a linear exchange economy with a continuum of agents. We first state the model and give conditions of an increasing strength for existence, uniqueness and continuity of equilibrium prices. Then, if we restrict ourselves to economies with essentially bounded initial endowments and if we assume that there is, from the point of view of preferences, only a finite number of types of agents, we show that, on an open dense subset of the space of initial endowments, the equilibrium price vector is an infinitely differentiable function of the initial endowments. The proof of this claim is based on a formula allowing to compute the equilibrium price vector around a so-called “regular” endowment where it is known.     

A limit characterization of belief-free equilibrium payoffs in repeated games

The present paper studies repeated games with private monitoring, and characterizes the set of belief-free equilibrium payoffs in the limit as the discount factor approaches one and the noise on private information vanishes. Contrary to the conjecture by Ely et al. [J.C. Ely, J. Hörner, W. Olszewski, Belief-free equilibria in repeated games, Econometrica 73 (2005) 377-415], the equilibrium payoff set is computed by the same formula, no matter how many players there are. As an application of this result, a version of the folk theorem is established for N-player prisoner's dilemma games.     

Characterizations of bargaining solutions in production economies with unequal skills

In production economies with unequal skills, this paper characterizes bargaining solutions by using axioms on allocation rules rather than axioms on classical bargaining solutions. We introduce a new axiom, consistency w.r.t. technological innovations, so that the non-welfaristic characterizations of bargaining solutions in the production economies are provided. By the characterizations, we can classify the three bargaining solutions (the Nash, the Kalai-Smorodinsky, and the Egalitarian solutions) from the viewpoint of responsibility and compensation discussed by Dworkin.     

Core equivalence theorem with production

In production economies, the extent to which non-equilibria are blocked depends on the allocation of control rights among shareholders, because a blocking coalition's resources are affected by the firms it jointly owns with outsiders. We formulate a notion of blocking that takes such interdependency problem into account, and we prove an analog of the Debreu-Scarf theorem for replica production economies. Our theorem differs from theirs in using an additional assumption, which we argue is indispensable and is driven by the interdependency problem.     

Equilibrium theory with asymmetric information and with infinitely many commodities

The traditional deterministic general equilibrium theory with infinitely many commodities cannot cover economies with private information constraints on the consumption sets. We bring the level of asymmetric information equilibrium theory at par with that of the deterministic one. In particular, we establish results on equilibrium existence for exchange economies with asymmetric (differential) information and with an infinite dimensional commodity space. Our new equilibrium existence theorems include, as a special case, classical results, e.g. Bewley [Existence of equilibria in economies with infinitely many commodities, J. Econ. Theory 4 (1972) 514-540] or Mas-Colell [The price equilibrium existence problem in topological vector lattices, Econometrica 54 (1986) 1039-1053].     

Star-shapedness of Richter-Aumann integral on a measure space with atoms: theory and economic applications

This paper provides sufficient (as well as necessary) conditions for the integral of a correspondence defined on a measure space with atoms to exhibit star-shaped values. This result is used to analyze the existence of a Nash equilibrium in games with a measure space of agents with atoms and of a competitive equilibrium in economies with mixed markets. In either case it is shown that an exact equilibrium exists whenever atoms are “small enough”.     

Bargaining foundations of the median voter theorem

We give a game-theoretic foundation for the median voter theorem in a one-dimensional bargaining model based on Baron and Ferejohn's [D. Baron, J. Ferejohn, Bargaining in legislatures, Amer. Polit. Sci. Rev. 83 (1989) 1181-1206] model of distributive politics. We prove that as the agents become arbitrarily patient, the set of proposals that can be passed in any pure strategy, subgame perfect equilibrium collapses to the median voter's ideal point. While we leave the possibility of some delay, we prove that the agents' equilibrium continuation payoffs converge to the utility from the median, so that delay, if it occurs, is inconsequential. We do not impose stationarity or any other refinements. Our result counters intuition based on the folk theorem for repeated games, and it contrasts with the known result for the distributive bargaining model that as agents become patient, any division of the dollar can be supported as a subgame perfect equilibrium outcome.     

Coase theorem, complexity and transaction costs

This paper, by introducing complexity considerations, provides a dynamic foundation for the Coase theorem and highlights the role of transaction costs in generating inefficient bargaining/negotiation outcomes. We show, when the players have a preference for less complex strategies, the Coase theorem holds in negotiation models with repeated surplus and endogenous disagreement payoffs if and only if there are no transaction costs. Specifically, complexity considerations select only efficient equilibria in these models without transaction costs while every equilibrium induces perpetual disagreement and inefficiency with transaction costs. We also show the latter is true in the Rubinstein bargaining model with transaction costs.     

A qualitative approach to Markovian equilibrium in infinite horizon economies with capital

Using lattice programming and order theoretic fixpoint theory, we develop a new class of monotone iterative methods that provide a qualitative theory of Markovian equilibrium decision processes for a large class of infinite horizon economies with capital. The class of economies includes models with public policy, valued fiat money, monopolistic competition, production externalities, and various other nonconvexities in the production sets. The results can be adapted to construct symmetric Markov equilibrium in models with many agents and market incompleteness. As the methods are constructive, they provide the foundations for a rigorous analysis of numerical approximation schemes that study extremal Markovian equilibrium. Equilibrium comparative statics results relative to the space of economies are available. Of independent interest, we provide new conditions for preserving complementarity under maximization, and new generalized envelope theorems for nonconcave dynamic programming problems. Our fixed point algorithms are sharp, and are able to distinguish sufficient conditions under which Markovian equilibrium form a complete lattice of Lipschitz continuous, uniformly continuous and semicontinuous monotone functions as well as unique continuously differentiable equilibrium.     

On the uniqueness of fully informative rational expectations equilibria

Summary. This paper analyzes two equivalent equilibrium notions under asymmetric information: risk neutral rational expectations equilibria (rn-REE), and common knowledge equilibria. We show that the set of fully informative rn-REE is a singleton, and we provide necessary and sufficient conditions for the existence of partially informative rn-REE. In a companion paper (DeMarzo and Skiadas (1996)) we show that equilibrium prices for the larger class of quasi-complete economies can be characterized as rn-REE. Examples of quasi-complete economies include the type of economies for which demand aggregation in the sense of Gorman is possible (with or without asymmetric information), the setting of the Milgrom and Stokey no-trade theorem, an economy giving rise to the CAPM with asymmetric information but no normality assumptions, the simple exponential-normal model of Grossman (1976), and a case of no aggregate endowment risk. In the common-knowledge context, we provide necessary and sufficient conditions for a common knowledge posterior estimate, given common priors, to coincide with the full communication posterior estimate. Received: May 29, 1997; revised version: July 18, 1997     

A testable model of consumption with externalities

This paper presents a nonparametric model of interdependent preferences, where an individual's consumption may act as an externality on the preferences of other consumers. We assume that individual price consumption data is observed for all consumers. It is known that the general consumption model with externalities imposes few restrictions on the observed data, where the consistency requirement is Nash rationalizability. We motivate potential games as an important sub class of games where the family of concave potential games is refutable and imposes stronger restrictions on observed data. We use this framework to extend the analysis of Brown and Matzkin [D. Brown, R. Matzkin, Testable restrictions on the equilibrium manifold, Econometrica 64 (1996) 1249-1262] on refutable pure exchange economies to pure exchange economies with externalities. Finally, we discuss an application of this model to inter-household consumption data.     

Trading with a common agent under complete information: A characterization of Nash equilibria

We analyze an abstract model of trading where N principals submit quantity-payment schedules that describe the contracts they offer to an agent, and the agent then chooses how much to trade with every principal. This represents a special class of common agency games with complete information. We study all the subgame perfect Nash equilibria of these games, not only truthful ones, providing a complete characterization of equilibrium payoffs. In particular, we show that the equilibrium that is Pareto-dominant for the principals is not truthful when there are more than two of them. We also provide a partial characterization of equilibrium strategies.     

Finitely repeated games with monitoring options

We study finitely repeated games where players can decide whether to monitor the other players? actions or not every period. Monitoring is assumed to be costless and private. We compare our model with the standard one where the players automatically monitor each other. Since monitoring other players never hurts, any equilibrium payoff vector of a standard finitely repeated game is an equilibrium payoff vector of the same game with monitoring options. We show that some finitely repeated games with monitoring options have sequential equilibrium outcomes which cannot be sustained under the standard model, even if the stage game has a unique Nash equilibrium. We also present sufficient conditions for a folk theorem, when the players have a long horizon.     

Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies

In this paper we consider a class of economies with a finite number of divisible commodities, linear production technologies, and indivisible goods and a finite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on one of the divisible commodities and on all the indivisible commodities, if each agent initially owns a sufficient amount of one of the divisible commodities, and if a “no production without input”-like assumption on the production sector holds, then there exists a competitive equilibrium for any economy in this class. The usual convexity assumption is not needed here. Furthermore, by imposing strong monotonicity on one of the divisible commodities we show that any competitive equilibrium is in the core of the economy and therefore the first theorem of welfare also holds. We further obtain a second welfare theorem stating that under some conditions a Pareto efficient allocation can be sustained by a competitive equilibrium allocation for some well-chosen redistribution of the total initial endowments. Journal of Economic Literature Classification Numbers: D4, D46, D5, D51, D6, D61.     

General equilibrium with nonconvexities and money

In a general-equilibrium economy with nonconvexities, there are sunspot equilibria with good welfare properties; sunspots can ameliorate the effects of the nonconvexities. For these economies, we show that agents act as if they have quasi-linear utility functions. We use this result to construct a new model of monetary exchange along the lines of Lagos and Wright, where trade occurs in both centralized and decentralized markets, but instead of quasi-linear preferences we assume general preferences but with indivisible labor. This suggests that modern monetary theory is more robust than one might have thought. It also constitutes progress on the classic problem of integrating monetary economics and general-equilibrium theory.