Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor

In this paper, we provide a set of sufficient conditions under which recursive competitive equilibrium exists and is unique for a large class of distorted dynamic equilibrium models with capital and elastic labor supply. We develop a lattice based approach to the problem. The class of economies for which we are able to obtain our existence and uniqueness result is considerably larger than those considered in previous work. We conclude by applying the new results to some important examples of monetary economies often used in applied work. Journal of Economic Literature Classification Numbers: C62, D51, D90, E10.     

On the nonexistence of recursive equilibrium in stochastic OLG economies

We study a class of stochastic Overlapping generations (OLG) economies that have one-memory equilibria, that is equilibria that are determined by the current and past realizations of the states of uncertainty. This class is negligible, but important. In particular, it contains all the known examples of nonexistence of recursive equilibrium. We show that, within this restricted domain, the existence of recursive equilibrium is actually typical, and such examples are therefore nonrobust. We thank Felix Kubler, Herakles Polemarchakis and Steve Spear for many useful discussions. This paper was started while the first author was visiting Columbia Business School.     

Equilibrium Prices When the Sunspot Variable Is Continuous

We analyze sunspot-equilibrium prices in nonconvex economies with perfect markets and a continuous sunspot variable. Our primary result is that every sunspot equilibrium allocation can be supported by prices that, when adjusted for probabilities, are constant across states. This result extends to the case of a finite number of equally-probable states under a nonsatiation condition, but does not extend to general discrete state spaces. We use our primary result to establish the equivalence of the set of sunspot equilibrium allocations based on a continuous sunspot variable and the set of lottery equilibrium allocations. Journal of Economic Literature Classification Numbers: D51, D84, E32.     

Co-ordination, Spillovers, and Cheap Talk

We analyze the role of cheap-talk in two player games with one-sided incomplete information. We identify conditions under which (1) players can fully communicate and coordinate on efficient Nash equilibria of the underlying complete information game; and (2) players cannot communicate so cheap-talk does not alter the equilibrium set of the Bayesian game. We present examples that illustrate several issues that arise when there is two-sided incomplete information. Journal of Economic Literature Classification Numbers: C72, D82.     

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 in economies with adverse selection

We model economies of adverse selection as Arrow–Debreu economies. In the spirit of Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we identify the consumption set of the individuals with the set of lotteries over net transfers. Thus, prices are linear in lotteries, but they may be non linear in commodity bundles. First, we study a weak equilibrium notion by viewing the economy of adverse selection as a pure exchange economy. The weak equilibrium set is non empty, but some of the allocations may be inefficient, and the equilibria indeterminate. Second, following Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we introduce an intermediary (firm) supplying feasible and incentive compatible measures. Equilibria are constrained efficient, but the equilibrium set is empty for an open set of economies containing the Rothschild and Stiglitz insurance economies. The research of A. Rustichini was supported by the NSF grant NSF/SES-0136556.     

A Unifying Pair of Cournot-Nash Equilibrium Existence Results

For games with a measure space of players a tandem pair, consisting of a mixed and a pure Cournot-Nash equilibrium existence result, is presented. Their generality causes them to be completely mutually equivalent. This provides a unifying pair of Cournot-Nash existence results that goes considerably beyond the central result of E. J. Balder (1995, Int. J. Game Theory24, 79-94, Theorem 2.1). The versatility of this pair is demonstrated by the following new applications: (i) unification and generalization of the two equilibrium distribution existence results by K. P. Rath (1996, J. Math. Econ.26, 305-324) for anonymous games, (ii) generalization of the equilibrium existence result of T. Kim and N. C. Yannelis (1997, J. Econ. Theory77, 330-353) for Bayesian differential information games, (iii) inclusion of the Bayesian Nash equilibrium existence results of P. R. Milgrom and R. J. Weber (1985, Math. Oper. Res.10, 619-632) and E. J. Balder (1988, Math. Operations Res.13, 265-276) for games with private information in the sense of J. C. Harsanyi (1967, Manage. Sci.14, 159-182). Journal of Economic Literature Classification Number: C72.     

Is dynamic general equilibrium a theory of everything?

Should we interpret the contributions of Edward C. Prescott and his collaborators, especially Finn Kydland and Rajnish Mehra, to dynamic general equilibrium as just a mathematical restatement of pre-Keynesian business cycle theory in the language of Arrow and Debreu? This essay advances the contrary view that Prescott has been laying the foundations for a theory of everything in macroeconomics that will stretch well beyond the frictionless environments treated in its early version. A theory of everything is an attempt to explain key empirical observations in nearly every subfield of macroeconomics from a simple, logically coherent conceptual platform with a minimum of institutional detail. After reviewing the current state of Prescott’s agenda, we examine several examples of dynamic equilibrium in economies with constant returns to scale, complete markets, idiosyncratic productivity shocks, and limited capital mobility. These examples suggest that the Solow residual controls the entire path of aggregate output if redefined more broadly to include financial, distributional and institutional variables; that the discount factor used in pricing streams of income will shift autonomously over time in response to endogenous changes in the set of unconstrained asset traders; and that a dynamic general equilibrium model with substantive frictions in financial markets goes some distance towards a joint account of well-known empirical anomalies in growth, business cycles, and asset returns.     

Time-inconsistent preferences in a general equilibrium model

This paper introduces time-inconsistent preferences in a multicommodity general equilibrium framework with incomplete markets. The standard concept of competitive equilibrium is extended in order to allow for changes in intertemporal preferences. Depending on whether or not agents recognize that their intertemporal preferences change, agents are called sophisticated or naïve. This paper presents competitive equilibrium notions for economies with naïve agents and economies with sophisticated agents and provides assumptions under which both types of equilibria exist. Surprisingly, the set of naïve equilibria in societies populated by time-consistent households is not allocationally equivalent to the set of competitive equilibria. For sophisticated equilibria, the equivalence holds. Time-inconsistency also raises conceptual issues about the appropriate concept of efficiency. Choices have to be made concerning the incorporation of future preferences and the appropriate instruments to create Pareto improvements. For both naïve and sophisticated societies, we present four possible efficiency concepts. Suitable conditions are specified for which both naïve and sophisticated equilibria satisfy appropriate efficiency concepts.     

Cournot-Nash and Lindahl equilibria in pure public “bad” economies

Summary. Using a general equilibrium framework, this paper analyzes the equilibrium provision of a pure public bad commodity (for example pollution). Considering a finite economy with one desired private good and one pure public “bad” we explicitly introduce the concept of Lindahl equilibrium and the Lindahl prices into a pure public bad economy. Then, the Lindahl provision is analyzed and compared with the Cournot-Nash provision. The main results for economies with heterogeneous agents state that the asymptotic Lindahl allocation of the pure public bad is the null allocation. In contrast, the asymptotic Cournot-Nash provision of the public bad might approach infinity. Other results were obtained in concert with the broad analysis of the large finite economies with pure public bad commodities. Received: July 26, 2001; revised version: March 12, 2002 RID="*" ID="*" We are indebt to Nicholas Yannelis and anonymous referee for their valuable comments and suggestions. Correspondence to: B. Shitovitz     

Search cost,trading strategies and optimal market structure

The theory of Walrasian equilibrium yields a set of prices at which the aggregate competitive demand for each commodity equals its aggregate competitive supply. However, even at equilibrium prices the theory of competitive equilibrium does not explicitly offer explanation regarding the manner in which trades are actually executed. This paper considers a model where trade takes place in a decentralized fashion and examines in a dynamic game-theoretic framework, the role of social institution of money and markets in facilitating exchange. The steady state Nash equilibrium derived in the paper demonstrates how, depending on the level of transaction costs associated with a market setup (synonymously, trading posts to exchange possible pairs of goods) appropriate monetary trade emerges, which like a hub and spoke network (Starr and Stinchcombe, 1999) makes some markets non-functioning and in equilibrium only the markets having trade through the medium of exchange continue to exist. However, despite the obvious advantages of a market setup in reducing search costs, pure random search for a complementary trading partner (as considered by Ostroy and Starr, 1974; Kiyotaki and Wright , 1989; and others) prevails in many economies, especially, in many developing economies. This paper models this feature of developing economies by introducing differences in transaction costs across agents and shows why sustainable equilibria might exist exhibiting random search for certain commodities even in the presence of established markets.     

Existence of a Pareto-optimal equilibrium in nearly-stationary overlapping-generations economies

Summary In overlapping-generations models of fiat money, the existence of a Pareto-optimal equilibrium — which defines an optimal quantity of money — is more general than well-known counter-examples suggest. Those examples, having no optimal equilibrium just because there are small variations in households' tastes and endowments across generations, are not typical. On the contrary: For an open-dense, full-measure subset of smooth stationary economies and an open-dense subset of continuous stationary economies, introducing small variations in tastes and endowments across generations preserves the existence of an optimal equilibrium. Put simply, optimal equilibria generically exist for nearly-stationary economies.I thank Scott Freeman, Katsuhiko Kawai, and two referees for proofreading this text; all lead to clarifications.     

Kantian Equilibrium

Consider a game whose strategies are "contributions". A strategy profile is a Kantian equilibrium if  no  player would like  all  players to alter their contributions by the  same multiplicative factor.  Kantian equilibria are Pareto efficient. We characterize the allocation rules on several domains of environments that can be implemented as Kantian equilibria. The concept unifies the  proportional solution  on production economies and the  linear cost-share equilibrium  on public-good economies. We study Kantian equilibrium in the prisoner's dilemma, in a voting problem, and in a political economy where redistribution is the issue. The Kantian dictum engenders considerable but not unqualified cooperation.     

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     

Walras and Darwin: an odd couple?

General equilibrium theory and the evolutionary branches of economics and game theory take rather opposite positions in the spectrum covered by the economic science. However, we reveal and explore analogies between Darwinian dynamics and Walrasian tatonnement processes for pure exchange economies, as well as further analogies implied by these.     

On extensive form implementation of contracts in differential information economies

Summary. In the context of differential information economies, with and without free disposal, we consider the concepts of Radner equilibrium, rational expectations equilibrium, private core, weak fine core and weak fine value. We look into the possible implementation of these concepts as perfect Bayesian or sequential equilibria of noncooperative dynamic formulations. We construct relevant game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs. The possibility of implementing an allocation is related to whether or not it is incentive compatible. Implementation through an exogenous third party or an endogenous intermediary is also considered. Received: November 19, 2001; revised version: April 17, 2002 RID="*" ID="*" This paper comes out of a visit by Nicholas Yannelis to City University, London, in December 2000. We are grateful to Dr A. Hadjiprocopis for his invaluable help with the implementation of Latex in a Unix environment. We also thank Leon Koutsougeras and a referee for several, helpful comments. Correspondence to: N.C. Yannelis     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

Note on the non-existence of sunspot equilibrium

In this note, we emphasize the role of consumers’ risk aversion in the non-existence of sunspot equilibria in incomplete market economies. We prove that there are no sunspot equilibria if the fundamentals of the underlying economy admit a unique equilibrium for any distribution of endowments. This substantiates Mas-Colell’s (Economic analysis of markets and games: essays in honor of Frank Hahn. MIT, Cambridge, 1992) conjecture. We also prove that, in a two-consumer economy, no sunspot equilibrium exists under the more relaxed condition that the underlying economy admits a unique equilibrium for the initial endowment. This is a generalization of Corollaries 1 and 2 of Hens and Pilgrim (Econ Theory 24:583–602, 2004).      

Arrow-Debreu equilibria with asymptotically heterogeneous expectations exist

Summary. In infinite horizon economies only local equivalence of beliefs is needed to ensure the existence of an Arrow–Debreu equilibrium. In fact, agents can even disagree completely in the long run in the sense that asymptotically, their beliefs are singular. Received: November 3, 2000; revised version: February 13, 2002