Indeterminacy of intertemporal equilibria under imperfect competition

Summary. It is known that overlapping generations models with imperfectly competitive firms may exhibit a continuum of stationary equilibria. The reason of this indeterminacy is that different price expectation functions of consumers lead to different objective demand functions against which firms maximize. All these expectation functions fulfill perfect foresight in the equilibrium, but they can be arbitrary off the equilibrium. In this paper it is shown that it is not this arbitrariness which is responsible for the indeterminacy, but that the continuum of stationary equilibria emerges even if expectation functions are rational. Received: March 25, 1999; revised version: February 16, 2000     

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     

Temporary financial equilibrium

Summary. In a two-period pure exchange economy with financial assets, a temporary financial equilibrium is an equilibrium of the current spot and security markets given forecast functions of future prices and payoffs. The temporary equilibrium model can then be interpreted as an Arrow-Debreu economy where preferences depend on prices. This identification implies, among other consequences, the existence and the generic determinateness of the financial temporary equilibria associated with given forecast functions. Received: December 29, 1999; revised version: December 20, 2001     

General equilibrium and resource economics

Summary. For a number of reasons a large class of general equilibrium models from the field of resource economics does not allow for an equilibrium analysis along the lines of the theory of infinite dimensional commodity spaces. The reasons concern the choice of the commodity space and the applicability of properness assumptions with respect to preferences and the technology. This paper illustrates the difficulties and shows for a prototype model how the problems can successfully be tackled by the use of a limit argument on equilibria in the truncated economies. Received: May 2, 1996; revised version: May 13, 1998     

Common priors under incomplete information: a unification

Summary. While the meaningfulness of the common prior assumption (CPA) under incomplete information has been established recently by various authors, its epistemic rationale has not yet been adequately clarified. To do so, we provide a characterization of the CPA in terms of a new condition called “Mutual Calibration”, and argue that it constitutes a more transparent and more primitive formalization of the Harsanyi Doctrine than the existing characterizations. Our analysis unifies the understanding of the CPA under incomplete information and clarifies the role of higher-order expectations and of the difference between situations with only two and those with at least three agents. In the concluding section, the analysis is applied to the problem of defining Bayesian consistency of the intertemporal beliefs of a single-agent with imperfect memory. The CPA yields a notion of “Bayesian updating without a prior”. Received: March 24, 2000; revised version: April 27, 2000     

Information at equilibrium

Summary. In a game with rational expectations, individuals simultaneously refine their information with the information revealed by the strategies of other individuals. At a Nash equilibrium of a game with rational expectations, the information of individuals is essentially symmetric: the same profile of strategies is also an equilibrium of a game with symmetric information; and strategies are common knowledge. If each player has a veto act, which yields a minimum payoff that no other profile of strategies attains, then the veto profile is the only Nash equilibrium, and it is is an equilibrium with rational expectations and essentially symmetric information; which accounts for the impossibility of speculation. Received: June 20, 2001; revised version: January 9, 2002 RID="*" ID="*" We wish to thank Pierpaolo Battigalli, Fran?oise Forges, Franco Donzelli, Leonidas Koutsougeras, Aldo Rustichini, Rajiv Vohra and Nicholas Yannelis for their comments. Correspondence to: H. Polemarchakis     

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     

Moral hazard and general equilibrium in large economies

Summary. The paper analyzes a two period general equilibrium model with individual risk, aggregate uncertainty and moral hazard. There is a large number of households, each facing two individual states of nature in the second period. These states differ solely in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period each household chooses a non-observable action. Higher levels of action give higher probability of the good state of nature to occur, but lower levels of utility. Households' utilities are assumed to be separable in action and the aggregate uncertainty is independent of the individual risk. Insurance is supplied by a collection of firms who behave strategically and maximize expected profits taking into account that each household's optimal choice of action is a function of the offered contract. The paper provides sufficient conditions for the existence of equilibrium and shows that the appropriate versions of both welfare theorems hold. Received: December 7, 1998; revised version: October 25, 1999     

Nash equilibrium without mutual knowledge of rationality

Summary. In a Nash equilibrium, players' rationality is mutual knowledge. However, both intuition and experimental evidence suggest that players do not know for sure the rationality of opponents. This paper proposes a new equilibrium concept, cautious equilibrium, that generalizes Nash equilibrium in terms of preferences in two person strategic games. In a cautious equilibrium, players do not necessarily know the rationality of opponents, but they view rationality as infinitely more likely than irrationality. For suitable models of preference, cautious equilibrium predicts that a player might take a “cautious” strategy that is not a best response in any Nash equilibrium. Received: January 28, 1998; revised version October 2, 1998     

Limit-pricing as Bertrand equilibrium

Summary. We consider a Bertrand duopoly model with increasing returns to scale where one of the firms have a cost advantage and prices vary over a grid. We find that typically more than one equilibria exist. However, there are only two perfect equilibria. Moreover, as the size of the grid becomes small, both these equilibria converge to the limit-pricing outcome. Received: February 25, 2000; revised version: January 9, 2001     

Computable general equilibrium with financial markets

Summary. There are a wide variety of theoretical general equilibrium models with incomplete security markets. In this paper we give a general recipe for using homotopy algorithm to compute equilibria in these models. In many models, taxes, transaction-costs or other market frictions introduce the additional difficulty that equilibrium prices or choices (but not equilibrium allocations) may be undetermined. In order to demonstrate how these difficulties can be dealt with, we develop a globally convergent algorithm to compute equilibria in a model with cash-in-advance constraints, several goods and incomplete financial markets. Furthermore we describe how to implement the algorithm using a publicly available suite of subroutines for homotopy-pathfollowing. Received: October 1, 1999; revised version: December 16, 2000     

Non-computability of competitive equilibrium

Summary. We provide a “computable counterexample” to the Arrow-Debreu competitive equilibrium existence theorem [2]. In particular, we find an exchange economy in which all components are (Turing) computable, but in which no competitive equilibrium is computable. This result can be interpreted as an impossibility result in both computability-bounded rationality (cf. Binmore [5], Richter and Wong [35]) and computational economics (cf. Scarf [39]). To prove the theorem, we establish a “computable counterexample” to Brouwer's Fixed Point Theorem (similar to Orevkov [32]) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell [26], Geanakoplos [16], Wong [50]). Received: September 9, 1997; revised version: December 17, 1997     

An experimental test of observational learning under imperfect information

Summary. Nearly all observational learning models assume that individuals can observe all the decisions that have previously been made. In reality, such perfect information is rarely available. To explore the difference between observational learning under perfect and imperfect information, this paper takes an experimental look at a situation in which individuals learn by observing the behavior of their immediate predecessors. Our experimental design uses the procedures of Çelen and Kariv [9] and is based on the theory of Çelen and Kariv [10]. We find that imitation is much less frequent when subjects have imperfect information, even less frequent than the theory predicts. Further, while we find strong evidence that under perfect information a form of generalized Bayesian behavior adequately explains behavior in the laboratory, under imperfect information behavior is not consistent even with this generalization of Bayesian behavior.Received: 29 January 2002, Revised: 12 May 2004, JEL Classification Numbers: C92, D8. Correspondence to: Boaçhan ÇelenWe completed most of this paper when we were both graduate students at New York University. This research was supported by the Center for Experimental Social Sciences (C.E.S.S.) and the C.V. Starr Center for Applied Economics at New York University. We are grateful to Andrew Schotter for his guidance and to an anonymous referee for his comments. We benefited from the expositional suggestions of William Baumol. We also acknowledge helpful discussions of Colin Camerer, Liran Einav, Xavier Gabaix, Douglas Gale, Charles Holt, David Laibson, and Matthew Rabin. We also benefited from suggestions by the participants of the 2002 International ESA Meeting and seminars at several universities.     

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     

The Borda rule,Condorcet consistency and Condorcet stability

Summary. The Borda rule is known to be the least vulnerable scoring rule to Condorcet inconsistency, Saari (2000). Such inconsistency occurs when the Condorcet winner (the alternative which is preferred to any other alternative by a simple majority) is not selected by the Borda rule. This note exposes the relationship between the Borda rule and the Condorcet q-majority principle as well as the Condorcet q-majority voting rule. The main result establishes that the Borda rule is Condorcet q-majority consistent when where k is the number of alternatives. The second result establishes that is the minimal degree of majority decisiveness corresponding to the Borda rule under sincere voting. The same majority is required to ensure decisiveness under the Borda rule and to ensure that a q-rule (the generalized q-majority Condorcet rule) is a voting rule. Received: April 8, 2002; revised version: July 17, 2002 Correspondence to:S. Nitzan     

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     

Currency restrictions,government transaction policies and currency exchange

Summary. We study how currency restrictions and government transaction policies affect the values of fiat currencies in a two country, divisible good, search model. We show that these policies can generate equilibria where both currencies circulate as medium of exchange and where currency exchange occurs between citizens of different countries. Restrictions on the internal use of foreign currency can cause the domestic currency to be relatively more valuable to domestic agents while taxes on domestic currency create an incentive for home agents to hold foreign currency. We demonstrate that some policies increase prices and lower welfare while others do the reverse. Received: September 5, 2001; revised version: March 1, 2002     

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     

Peer group effects in applied general equilibrium

Summary. In this paper, I develop an applied general equilibrium environment with peer group effects. The application I consider is schooling. The framework used here is general equilibrium with clubs. I establish the existence of equilibrium for the economy with a finite number of school types. This result is then extended to the case where the set of school types is a continuum. The two welfare theorems are shown to hold for both economies. To compute the equilibrium, I construct a Negishi mapping from the set of weights on individual type's utility to the set of transfers that support the corresponding Pareto allocations as competitive equilibria with transfers. Because this mapping is a correspondence, a version of Scarf's algorithm is used to find a competitive equilibrium. Received: June 9, 1999; revised version: March 13, 2000     

An experimental study of information and mixed-strategy play in the three-person matching-pennies game

Summary. Recent experiments on mixed-strategy play in experimental games reject the hypothesis that subjects play a mixed strategy even when that strategy is the unique Nash equilibrium prediction. However, in a three-person matching-pennies game played with perfect monitoring and complete payoff information, we cannot reject the hypothesis that subjects play the mixed-strategy Nash equilibrium. Given this support for mixed-strategy play, we then consider two qualitatively different learning theories (sophisticated Bayesian and naive Bayesian) which predict that the amount of information given to subjects will determine whether they can learn to play the predicted mixed strategies. We reject the hypothesis that subjects play the symmetric mixed-strategy Nash equilibrium when they do not have complete payoff information. This finding suggests that players did not use sophisticated Bayesian learning to reach the mixed-strategy Nash equilibrium. Received: August 9, 1996; revised version: October 21, 1998