Balancedness and the core in economies with asymmetric information

Summary. A condition is given that is equivalent to balancedness of all NTU-games derived from an exchange economy with asymmetric information when endowments are variable. The condition is applicable to the ex-ante model with expected utilities, but also to the more general model of Arrow-Radner type economies without subjective probabilities. Differences in the interpretation of measurability assumptions between these two models are discussed, and another model with information consistent utility functions is developed in which the result would also hold. Received: December 12, 2001; revised version: November 1, 2002 RID="*" ID="*"I thank two anonymous referees whose comments led to an improvement of the paper.     

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     

Market games with asymmetric information: the core

This paper concerns cores of economies with asymmetric information. Alternative definitions of the information available to traders in coalitions and the cooperative games they generate are analyzed. An important technical result states that such NTU games in characteristic function form are well defined. Properties of various cores with asymmetric information are examined. Sufficient conditions on information sharing rules are provided for the induced games to be totally balanced or balanced, so that their cores are nonempty. Incentive compatibility issues are considered. Finally, a perspective on this research area is provided.     

Exchange economies with asymmetric information: competitive equilibrium and core

Summary. A replica theorem is shown to hold for exchange economies with asymmetric information. In a replicated exchange economy with asymmetric information the set of all core elements with equal treatment is nonempty, but it is in general only a subset of the core. Nevertheless, the replica theorem and the presence of at least one core element with equal treatment suffice to show existence of a competitive quasi-equilibrium. Conditions on the initial endowments and the communication system are given to ensure that every competitive quasi-equilibrium is a competitive equilibrium.Received: 24 February 2003, Revised: 3 July 2003JEL Classification Numbers: C70, D50, D82.I thank an anonymous referee whose comments led to an improvement of the paper.     

The core of an exchange economy with asymmetric information

This paper studies the core of an exchange economy in which agents are asymmetrically informed about states of nature. An agent's information is modelled as part of his consumption set and thus as part of his consumption plans. If an agent joins a coalition, his information changes according to an exogenously given information rule, a concept introduced by B. Allen. It is shown that an exchange economy with asymmetric information generates a well defined cooperative game and that the core of this game and thus the core of the underlying economy is nonempty. In contrast to recent results, this holds independently of the given information rule.     

Competitive and core allocations in large economies with differential information

Summary. We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is “irreducible”, then a competitive equilibrium, in the sense of Radner (1968, 1982), exists. Moreover, the set of competitive equilibrium allocations coincides with the “private core” (Yannelis, 1991). We also show that the “weak fine core” of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy. Received March 22, 2000; revised version: May 1, 2000     

Non-myopic learning in differential information economies: the core

Summary. We study the process of learning in a differential information economy, with a continuum of states of nature that follow a Markov process. The economy extends over an infinite number of periods and we assume that the agents behave non-myopically, i.e., they discount the future. We adopt a new equilibrium concept, the non-myopic core. A realized agreement in each period generates information that changes the underlying structure in the economy. The results we obtain serve as an extension to the results in Koutsougeras and Yannelis (1999) in a setting where agents behave non-myopically. In particular, we examine the following two questions: 1) If we have a sequence of allocations that are in an approximate non-myopic core (we allow for bounded rationality), is it possible to find a subsequence that converges to a non-myopic core allocation in a limit full information economy? 2) Given a non-myopic core allocation in a limit full information economy can we find a sequence of approximate non-myopic core allocations that converges to that allocation? Received: May 25, 1999; revised version: August 9, 1999     

The core in an oligopoly market with indivisibility

Summary. This paper studies the core in an oligopoly market with indivisibility. It provides necessary and sufficient conditions for core existence in a general m-buyer n-seller market with indivisibility. When costs are dominated by opportunity costs (i.e., a firm's variable costs are sufficiently small), the core condition can be characterized by the primitive market parameters. In a 3-2 market with opportunity cost, the core is non-empty if and only if the larger seller's opportunity cost is either sufficiently large or sufficiently small. Received: June 9, 1999; revised version: October 22, 1999     

The bargaining set of a large economy with differential information

Summary. We study the Mas-Colell bargaining set of an exchange economy with differential information and a continuum of traders. We established the equivalence of the private bargaining set and the set of Radner competitive equilibrium allocations. As for the weak fine bargaining set, we show that it contains the set of competitive equilibrium allocations of an associated symmetric information economy in which each trader has the “joint information” of all the traders in the original economy, but unlike the weak fine core and the set of fine value allocations, it may also contain allocations which are not competitive in the associated economy. Received: February 15, 1999; revised version: August 9, 1999     

Uncertainty and insurance in strategic market games

Summary. For perfectly competitive economies under uncertainty, there is a well-known equivalence between a formulation with contingent goods and one with state-specific securities followed by spot markets for goods. In this paper, I examine whether this equivalence carries over to a particular form of imperfect competition. Specifically, I look at three Shapley-Shubik strategic market games: one with contingent commodities, one with Arrow securities traded under imperfect competition and one with Arrow securities traded under perfect competition. First I compare the feasibility constraints of these three games. Then I compare their equilibrium sets. As in Peck and Shell (1989), the only common equilibria between the first and the second game are those which involve no transfer of income across states. However, if the securities markets are competitive, then the set of equilibria of the contingent commodities game and the securities game coincide. Received: June 16, 1997; revised version: April 30, 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     

Incomplete risk sharing arrangements and the value of information

Summary. The paper constructs a theoretical framework in which the value of information in general equilibrium is determined by the interaction of two opposing mechanisms: first, more information about future random events leads to better individual decisions and, therefore, higher welfare. This is the ‘Blackwell effect’ where information has positive value. Second, more information in advance of trading limits the risk sharing opportunities in the economy and, therefore, reduces welfare. This is the ‘Hirshleifer effect’ where information has negative value. We demonstrate that in an economy with production information has positive value if the information refers to non-tradable risks; hence, such information does not destroy the Blackwell theorem. Information which refers to tradable risks may invalidate the Blackwell theorem if the consumers are highly risk averse. The critical level of relative risk aversion beyond which the value of information becomes negative is less than 0.5. Received: May 14, 2001; revised version: March 5, 2002     

Ex ante contracting with endogenously determined communication plans

Summary. In this paper we introduce a new model of ex ante contracting for economies with asymmetric information to examine endogenously determined communication plans for information sharing in the interim stage. In contrast to the models used in previous research, in the present model agents negotiate not only on a contract of state contingent allocations but also on a communication plan, a set of rules describing how agents will reveal part of their private information at the interim stage to execute the trade contracts. We prove a result about the nested structure of the set of allocations implementable by various communication plans and establish the existence of core strategies for this cooperative game under various regularity conditions. Received: 4 March 1998; revised version: 17 September 1999     

Equilibrium selection in coordination games with simultaneous play

Summary. We apply the dynamic stochastic framework proposed in recent evolutionary literature to a class of coordination games played simultaneously by the entire population. In these games payoffs, and hence best replies, are determined by a summary statistic of the population strategy profile. We demonstrate that with simultaneous play, the equilibrium selection depends crucially on how best responses to the summary statistic remain piece-wise constant. In fact, all the strict Nash equilibria in the underlying stage game can be made stochastically stable depending on how the best response mapping generates piece-wise constant best responses. Received: February 12, 2001; revised version: October 29, 2001     

Risk aversion and incentive compatibility with ex post information asymmetry

Summary. The paper extends Diamond's (1984) analysis of financial contracting with information asymmetry ex post and endogenous “bankruptcy penalties” to allow for risk aversion of the borrower. The optimality of debt contracts, which Diamond obtained for the case of risk neutrality, is shown to be nonrobust to the introduction of risk aversion. This contrasts with the costly state verification literature, in which debt contracts are optimal for risk averse as well as risk neutral borrowers. Received: December 7, 1998; revised version: June 9, 1999     

Fictitious play in ‘one-against-all’ multi-player games

Summary. A compound game is an (n + 1) player game based on n two-person subgames. In each of these subgames player 0 plays against one of the other players. Player 0 is regulated, so that he must choose the same strategy in all n subgames. We show that every fictitious play process approaches the set of equilibria in compound games for which all subgames are either zero-sum games, potential games, or games. Received: July 18, 1997; revised version: December 4, 1998     

Coalitional Bayesian Nash implementation in differential information economies

Summary. A mechanism coalitionally implements a social choice set if any outcome of the social choice set can be achieved as a coalitional Bayesian Nash equilibrium of a mechanism and vice versa. We say that a social choice set is coalitionally implementable if there is a mechanism which coalitionally implements it. Our main theorem proves that a social choice set is coalitionally implementable if and only if it is interim individually rational, interim efficient, coalitional B ayesian incentive compatible, and satisfies a coalitional Bayesian monotonicity condition as well as a closure condition. As an application of our main result, we show that the private core and the private Shapley value of an economy with differential information are coalitionally implementable. Received: January 12, 1998; revised version: March 30, 2000     

Probability of survival in a random exchange economy with dependent agents

Summary. In this paper I analyze the general equilibrium in a random Walrasian economy. Dependence among agents is introduced in the form of dependency neighborhoods. Under the uncertainty, an agent may fail to survive due to a meager endowment in a particular state (direct effect), as well as due to unfavorable equilibrium price system at which the value of the endowment falls short of the minimum needed for survival (indirect terms-of-trade effect). To illustrate the main result I compute the stochastic limit of equilibrium price and probability of survival of an agent in a large Cobb-Douglas economy. Received June 7, 2001; revised version: January 7, 2002 RID="*" ID="*" I would like to thank Mukul Majumdar and Thomas DiCiccio for helpful discussion and an anonymous referee for valuable comments and suggestions.     

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     

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