Incentive compatible core and competitive equilibria in differential information economies

Summary. If the allocations of a differential information economy are defined as incentive compatible state-contingent lotteries over consumption goods, competitive equilibrium allocations exist and belong to the (ex ante incentive) core. Furthermore, any competitive equilibrium allocation can be viewed as an element of the core of the n-fold replicated economy, for every n. The converse holds under the further assumption of independent private values but not in general, as shown by a counter-example. Received: August 9, 1999; revised version: September 12, 1999     

Walrasian versus quasi-competitive equilibrium and the core of a production economy

Summary. This paper presents very general conditions guaranteeing that a quasi-competitive equilibrium is a Walrasian equilibrium. We also develop a generalization (and a simplified proof) of Nikaidos and McKenzies extensions of the classic Debreu-Scarf theorem on core convergence, and apply the first result to obtain an equivalence between the set of Edgeworth equilibria and the set of Walrasian equilibria in a production economy.Received: 6 September 2002, Revised: 14 November 2003, JEL Classification Numbers: C71, D50, D51.     

Decentralizing Edgeworth equilibria in economies with many commodities

Summary. This paper proves core-equivalence theorems for exchange economies without ordered preferences, defined on locally convex Riesz commodity spaces such that the price space is a lattice. Properness assumptions are borrowed from some recent equilibrium existence results. Received: January 15, 1998; revised version: August 19, 1998     

Core concepts in economies where information is almost complete

Summary. The paper analyzes the properties of cores with differential information, as economies converge to complete information. Two core concepts are investigated: the private core, in which agents' net trades are measurable with respect to agents' private information, and the incentive compatible core, in which coalitions of agents are restricted to incentive compatible allocations. Received: March 15, 2000; revised version: August 24, 2000     

Markov perfect equilibria in industries with complementarities

Summary.   This paper considers the existence and computation of Markov perfect equilibria in games with a “monotone” structure. Specifically, it provides a constructive proof of the existence of Markov perfect equilibria for a class of games in which a) there is a continuum of players, b) each player has the same per period payoff function and c) these per period payoff functions are supermodular in the player's current and past action and have increasing differences in the player's current action and the entire distribution of actions chosen by other players. The Markov perfect equilibria that are analyzed are symmetric, not in the sense that each player adopts the same action in any period, but rather in the sense that each player uses the same policy function. Since agents are typically distributed across many states they will typically take different actions. The formal environment considered has particular application to models of industries (or economies) in which firms face costs of price adjustment. It is in this context that the results are developed. Received: November 9, 1999; revised version: February 10, 2000     

Nash implementation with a private good

Summary. I construct a general model of social planning problems, including mixed production economies and regulatory problems with negative externalities as special cases, and I give simple mechanisms for Nash implementation under three increasingly general sets of assumptions. I first construct a continuous mechanism to implement the (constrained) Lindahl allocations of an economy, and I then extend this to arbitrary social choice rules based on prices. I end with a mechani sm to implement any monotonic social choice rule, assuming only the existence of a private (not necessarily transferable) good. In that general case, each agent simply reports an upper contour set, an outcome, and I need two agents to make binary numerical announcements. I do not require the usual no-veto-power condition. Received: February 19, 1998; revised version: January 30, 2002     

Inefficient Markov perfect equilibria in multilateral bargaining

We study a complete-information alternating-offer bargaining game in which one “active” player bargains with each of a number of other “passive” players one at a time. In contrast to most existing models, the order of reaching agreements is endogenously determined, hence the active player can “play off” some passive players against others by m oving back and forth bargaining with the passive players. We show that this model has a finite number of Markov Perfect Equilibria, some of which exhibiting wasteful delays. Moreover, the maximum number of delay periods that can be supported in Markov Perfect Equilibria increases in the order of the square of the number of players. We also show that these results are robust to a relaxing of the Markov requirements and to more general surplus functions. Received: November 19, 2001; revised version: August 20, 2002 RID="*" ID="*"This paper grew out of my dissertation submitted to Stanford University. I am deeply indebted to my advisor, Paul Milgrom, for his insights and guidance. I would also like to thank Douglas Bernheim, Sushil Bikhchandani, Harold Demsetz, Bryan Ellickson, Avner Greif, Peter Hammond, David Levine, Bentley Macleod, Joe Ostroy, John Pencavel, Jean-Laurent Rosenthal, David Starrett, Robert Wilson, Bill Zame and especially John Riley and Jeff Zwiebel for their helpful comments. I am grateful to an anonymous referee for extremely constructive suggestions.     

A note on asymmetric and mixed strategy equilibria in the search-theoretic model of fiat money

Summary. The simple search-theoretic model of fiat money has three symmetric Nash equilibria: all agents accept money with probability 1; all agents accept money with probability 0; and all agents accept money with probability y in (0,1). Here I construct an asymmetric pure strategy equilibrium, payoff-equivalent to the symmetric mixed strategy equilibrium, where a fraction N in (0,1) of agents always accept money and 1-N never accept money. Counter to what has been conjectured previously, I find N > y. I also introduce evolutionary dynamics, and show that the economy converges to monetary exchange iff the initial proportion of agents accepting money exceeds N. Received: September 10, 1997; revised version: April 24, 1998     

Inefficient ex-post equilibria in efficient auctions

Summary. I consider a single-object English auction with two asymmetric bidders and show that it has a continuum of inefficient undominated ex-post equilibria. The result extends for the generalized VCG mechanism, Dasgupta-Maskin auction and, generally, for every auction that has an efficient ex-post equilibrium. Received: November 5, 2001; revised version: June 10, 2002 RID="*" ID="*"I am grateful to Vijay Krishna, Sergei Izmalkov and anonymous referee for many important comments.     

Resource-monotonic allocation when preferences are single-peaked

Summary. We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. Thomson (1994a), S?nmez (1994), and Moulin (1999) introduce three different resource-monotonicity conditions. In each characterization they derive, the axioms are independent. Under Pareto-optimality, the three resource-monotonicity conditions are equivalent. We investigate whether the interchange of these conditions still yields a valid characterization, and when the characterization still holds, whether it is a tight result or not. We strengthen each of the results, that is either the used resource-monotonicity condition can be replaced by a weaker one, or by using another resource-monotonicity condition, the result is not tight. Our main result is that when at least three agents are present, the class of fixed-path rationing methods is characterized by weak one-sided resource-monotonicity, strategy-proofness, and consistency. Received: April 24, 2000; revised version: April 10, 2001     

On the computation of stable sets and strictly perfect equilibria

Summary. In this paper a procedure is described that computes for a given bimatrix game all stable sets in the sense of Kohlberg and Mertens (1986). Further the procedure is refined to find the strictly perfect equilibria (if any) of such a game. Recieved: December 29, 1999; revised version: February 17, 2000     

Oligopoly equilibria in exchange economies: a limit theorem

In a pure exchange economy, agents have the possibility of behaving strategically by putting only a part of their initial endowments on the market. An oligopoly equilibrium is defined to be a Nash equilibrium of the game in which agents choose simultaneously quantities to be put on the market. It is proved that under standard hypotheses, the oligopoly equilibrium leads to the competitive equilibrium when the economy is replicated an infinite number of times. Received: May 26, 1999; revised version: April 3, 2000     

Generic inefficiency of equilibria in the general equilibrium model with incomplete asset markets and infinite time

Summary. We consider a Lucas asset-pricing model with heterogeneous agents, exogenous labor income, and a finite number of exogenous shocks. Although agents are infinitely lived, endowments and dividends are time-invariant functions of the exogenous shock alone and are thus restricted to lie in a finite-dimensional space; genericity analysis can be conducted on sets of zero Lebesgue measure. When financial markets are incomplete, that is, there are fewer financial securities than shocks, we show that generically in individual endowments all competitive equilibria are Pareto inefficient. Received: November 22, 1999; revised version: March 4, 2002 RID="*" ID="*" We are grateful to an anonymous referee for very insightful comments on earlier drafts.     

Long run equilibria in an asymmetric oligopoly

Summary. Consider an oligopolistic industry composed of two groups (or populations) of firms, the low cost firms and the high cost firms. The firms produce a homogeneous good. I study the finite population evolutionarily stable strategy defined by Schaffer (1988), and the long run equilibrium in the stochastic evolutionary dynamics based on imitation and experimentation of strategies by firms in each group. I will show the following results. 1) The finite population evolutionarily stable strategy (ESS) output is equal to the competitive (or Walrasian) output in each group of the firms. 2) Under the assumption that the marginal cost is increasing, the ESS state is the long run equilibrium in the stochastic evolutionary dynamics in the limit as the output grid step, which will be defined in the paper, approaches to zero. Received: September 19, 1997; revised: June 18, 1998     

A new look for Stackelberg-Cournot equilibria in oligopolistic markets

Summary. This note deals with Cournot type oligopolies in which the market clearing price occasionally may be non-unique. A Stackelberg leading producer is present. Given that setting we explore continuity properties of the followers' reaction and provide sufficient conditions for existence of equilibrium. Received: June 20, 2000; revised version: April 24, 2001     

Existence and optimality of oligopoly equilibria in linear exchange economies

Summary. We consider a linear exchange economy and its successive replicas. We study the notion of Cournot-Walras equilibrium in which the consumers use the quantities of commodities put on the market as strategic variables. We prove that, generically, if the number of replications is large enough but finite, the competitive behaviour is an oligopoly equilibrium. Then, under a mild condition, which may be interpreted in terms of market regulation and/or market activity, we show that any sequence of oligopoly equilibria of successive replica economies converges to the Walrasian outcome and furthermore that every oligopoly equilibrium of large, but finite, replica is Pareto optimal. Consequently, under the same assumptions on the fundamentals of the economy, one has an asymptotic result on the convergence of oligopoly equilibria to the Walras equilibrium together with a generic existence result for the Cournot-Walras. Received: June 20, 2002; revised version: November 20, 2002 RID="*" ID="*" Part of this paper was written while the second author was visiting the Universidad de Vigo. The support of the department of mathematics is gratefully acknowledged. Correspondence to: J.M. Bonnisseau     

Production equilibria in vector lattices

The general purpose of this paper is to prove quasiequilibrium existence theorems for production economies with general consumption sets in an infinite dimensional commodity space, without assuming any monotonicity of preferences or free-disposal in production. The commodity space is a vector lattice commodity space whose topological dual is a sublattice of its order dual. We formulate two kinds of properness concepts for agents' preferences and production sets, which reduce to more classical ones when the commodity space is locally convex and the consumption sets coincide with the positive cone. Assuming properness allows for extension theorems of quasiequilibrium prices obtained for the economy restricted to some order ideal of the commodity space. As an application, the existence of quasiequilibrium in the whole economy is proved without any assumption of monotonicity of preferences or free-disposal in production. Received: March 9, 1999; revised version: September 4, 2000     

On games with identical equilibrium payoffs

Summary. This paper compares the sets of Nash, coalition- proof Nash and strong Nash equilibrium payoffs of normal form games which are closely related. We propose sufficient conditions for equivalent or closely related games to have identical sets of equilibrium payoffs. Received: April 23, 1999; revised version: November 23, 1999