Monetary equilibrium in an overlapping generations model with productive capital

Summary We study perfect foresight competitive equilibrium in an overlapping generations model with productive capital and a fixed nominal stock of money. We obtain almost-complete characterizations of (a) the existence of a monetary equilibrium from an arbitrary initial capital stock, and (b) the existence of anefficient monetary equilibrium from an arbitrary initial capital stock. When the initial capital stock is no larger than the golden rule stock, the necessary and sufficient condition for both (a) and (b) is the dynamic inefficiency (in the sense of Malinvaud) of the autarkic (or nonmonetary) equilibrium from the same initial stock. However, this condition, though necessary, isnot sufficient for the existence of a monetary equilibrium when the initial stock exceeds the golden rule stock (and still more conditions are needed for anefficient monetary equilibrium to exist). We provide characterizations for these cases, and as corollaries obtain examples in which (a) the nonmonetary equilibrium is inefficient but no monetary equilibrium exists, and (b) monetary equilibria exist but no efficient monetary equilibrium does.We are grateful to a co-editor and an anonymous referee for comments that greatly improved the exposition in the paper.     

Markov Perfect Equilibrium: I. Observable Actions

We define Markov strategy and Markov perfect equilibrium (MPE) for games with observable actions. Informally, a Markov strategy depends only on payoff-relevant past events. More precisely, it is measurable with respect to the coarsest partition of histories for which, if all other players use measurable strategies, each player's decision-problem is also measurable. For many games, this definition is equivalent to a simple affine invariance condition. We also show that an MPE is generically robust: if payoffs of a generic game are perturbed, there exists an almost Markovian equilibrium in the perturbed game near the initial MPE. Journal of Economic Literature Classification Numbers: C72, C73.     

Consumer search markets with costly revisits

This paper characterizes equilibrium outcomes in consumer search markets taking the cost of going back to stores already searched explicitly into account. We show that the optimal sequential search rule under costly revisits is very different from the traditional reservation price rule in that it is non-stationary and not independent of previously sampled prices. We explore the implications of costly revisits on market equilibrium in two celebrated search models. In the Wolinsky model, some consumers search beyond the first firm. In this class of models, costly revisits do make a substantive difference and their impact can be of the same order of magnitude as the initial search cost. In the Stahl oligopoly search model where consumers do not search beyond the first firm, there remains a unique symmetric equilibrium that has firms use pricing strategies that are identical to the perfect recall case.     

A “Super” Folk Theorem for dynastic repeated games

We analyze dynastic repeated games. These are repeated games in which the stage game is played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. Individuals live one period and do not observe the history of play that takes place before their birth, but instead create social memory through private messages received from their immediate predecessors. Under mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained by sequential equilibria of the dynastic repeated game with private communication. In particular, the result applies to any stage game with n  ≥  4 players for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize fully the conditions under which a sequential equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a subgame perfect equilibrium of the standard repeated game. For this to be the case it must be that the players’ equilibrium beliefs violate a condition that we term “inter-generational agreement.” A previous version of this paper was circulated as Anderlini et al. (2005). We are grateful to Jeff Ely, Leonardo Felli, Navin Kartik, David Levine, Stephen Morris, Michele Piccione, Andrew Postlewaite, Lones Smith and to seminar audiences at Bocconi, Cambridge, CEPR-Guerzensee, Chicago, Columbia, Edinburgh, Essex, Georgetown, Leicester, LSE, Northwestern, Oxford, Rome (La Sapienza), Rutgers, SAET-Vigo, Stanford, SUNY-Albany, UCL, UC-San Diego, Venice and Yale for helpful feedback.     

Endogenous Firm Objectives

We analyze the behavior of a monopolistic firm in general equilibrium when the firm's decisions are taken through shareholder voting. We show that, depending on the underlying distribution, rational voting may imply overproduction as well as underproduction, relative to the efficient level. Any initial distribution of shares is an equilibrium, if individuals do not recognize their influence on voting when trading shares. However, when they do, and there are no short–selling constraints, the only equilibrium is the efficient one. With short–selling constraints typically underproduction occurs. It is not market power itself causing underproduction, but the inability to perfectly trade the rights to market power.     

A Bayesian Model of Voting in Juries

We model voting in juries as a game of incomplete information, allowing jurors to receive a continuum of signals. We characterize the unique symmetric equilibrium of the game, and give a condition under which no asymmetric equilibria exist under unanimity rule. We offer a condition under which unanimity rule exhibits a bias toward convicting the innocent, regardless of the size of the jury, and give an example showing that this bias can be reversed. We prove a “jury theorem” for our general model: As the size of the jury increases, the probability of a mistaken judgment goes to zero for every voting rule except unanimity rule. For unanimity rule, the probability of making a mistake is bounded strictly above zero if and only if there do not exist arbitrarily strong signals of innocence. Our results explain the asymptotic inefficiency of unanimity rule in finite models and establishes the possibility of asymptotic efficiency, a property that could emerge only in a continuous model. Journal of Economic Literature Classification Numbers: C72, D72.     

Coalition Formation with Binding Agreements

We study coalition formation in "real time", a situation in which coalition formation is intertwined with the ongoing receipt of pay-offs. Agreements are assumed to be permanently binding: They can only be altered with the full consent of existing signatories. For characteristic function games we prove that equilibrium processes—whether or not these are history dependent—must converge to efficient absorbing states. For three-player games with externalities each player has enough veto power that a general efficiency result can be established. However, there exist four-player games in which all Markov equilibria are inefficient from every initial condition, despite the ability to write permanently binding agreements.     

A competitive model of economic geography

Summary. Most of the literature argues that competitive analysis has nothing interesting to say about location. This paper argues, to the contrary, that a competitive model can have something interesting to say about location, provided that locations are not identical and transportation costs are not zero. To do this, it constructs a competitive intertemporal general equilibrium model and applies it to a suggestive example of migration.Received: 25 August 2003, Revised: 18 December 2003, JEL Classification Numbers: D5, R0.Our interest in this topic has been stimulated over the years by many conversations with Marcus Berliant. We thank an anonymous referee for exceptionally careful and useful comments. Financial support from the UCLA Academic Committee on Research (Ellickson, Zame) and the National Science Foundation (Zame) is gratefully acknowledged. Views expressed here are those of the authors and do not necessary reflect the views of any funding agency.     

Fictitious Play in Extensive Form Games

This article analyzes the fictitious play process originally proposed for strategic form games by Brown (1951) and Robinson (1951). We interpret the process as a model of preplay thinking performed by players before acting in a one-shot game. This model is one of bounded rationality. We discuss how fictitious play should then be defined for extensive form games and conclude that this is somewhat problematic. We therefore study two alternative definitions. For either of these, under a weak condition of initial uncertainty, a convergence point of a fictitious play sequence is a sequential equilibrium. For generic games of perfect information initial uncertainty also implies convergence of fictitious play.Journal of Economic LiteratureClassification Number: C72.     

Supply and demand explanations and their ceteris paribusclauses

This paper argues that supply and demand explantions are causal explanations and that it is helpful to recognize this fact explicity, for then one can appreciate that the variables impounded in the ceteris paribusclauses attached to supply and demand curves are other causes. One can then specify clearly the conditions of membership in a ceteris pairbusclause: 1) include all those factors that within the given time period significantly affect the amount supplied or demanded but; 2) do not include any factors that themselves within the given time period significantly depend on the price of the particular commodity or service. Note the vague word ‘significantly’. If one insists on the general interdependencies established in general equilibrium analyses, one must reject partial equilibrium analyses altogether, but to do so would rule out work that may be enlightening and useful. Such theoretical purism is also indefensible, since general equilibrium analyse rely on similar causal approximations. This analyses of ceteris paribusclauses is helpful in understanding where supply and demand analysis or comparative statics goes wrong, as in traditional functional distribution theory.     

The One-Shot-Deviation Principle for Sequential Rationality

This article analyzes the fictitious play process originally proposed for strategic form games by Brown (1951) and Robinson (1951). We interpret the process as a model of preplay thinking performed by players before acting in a one-shot game. This model is one of bounded rationality. We discuss how fictitious play should then be defined for extensive form games and conclude that this is somewhat problematic. We therefore study two alternative definitions. For either of these, under a weak condition of initial uncertainty, a convergence point of a fictitious play sequence is a sequential equilibrium. For generic games of perfect information initial uncertainty also implies convergence of fictitious play.Journal of Economic LiteratureClassification Number: C72.     

Ex post implementation

We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and—in economic environments—sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is sufficient. Ex post monotonicity is satisfied in all single crossing environments with strict ex post incentive constraints.We show by means of two classic examples that ex post monotonicity does not imply nor is it implied by Maskin monotonicity. The single unit auction with interdependent valuations is shown to satisfy ex post monotonicity but not Maskin monotonicity. We further describe a Pareto correspondence that fails ex post monotonicity but satisfies Maskin monotonicity.     

Fractional cointegration,low frequency dynamics and long-run purchasing power parity: an analysis of the Australian dollar over its recent float

A relatively new but generalized concept of fractional cointegration is applied to shed some light on the validity of purchasing power parity (PPP) as a long-run equilibrium condition, by examining the long-run relationship between quarterly consumer price indices and bilateral exchange rates of the Australian dollar and seven major OECD trading partners, over Australia's recent float. The paper demonstrates that relaxing the condition that the residual from the cointegration equation must be a I(0) process, provides a wide range of cases of parity-reversion with processes that are CI(1,d) with 0 < d < 1. Findings tend to suggest that, while standard tests of cointegration fail to support cointegration between nominal exchange rates, domestic and foreign prices, and thus the empirical favour for PPP as a long-run phenomenon, the fractional cointegration analysis permits deviations from equilibrium to follow a fractionally integrated process and hence captures a much wider class of parity or mean-reversion behaviour. Results are mainly supportive of long-run PPP. Furthermore, an analysis of the short-run dynamics propelling the long-run relationship (through a VECM) reveals that domestic prices are consistently the initial receptor of an exogenous shock to the equilibrium and the long-run equilibrium is restored through the short-run adjustment of the nominal exchange rates. These findings are shown to hold clear policy implications.     

The Zilcha criterion for dynamic inefficiency

Summary. This paper reexamines the condition (1 + n), which Zilcha (1991) presents as a necessary and sufficient condition for dynamic inefficiency of stationary allocations in overlapping generation models with stochastic production. We show that this condition is necessary but not sufficient for a stationary allocation to be dynamically inefficient by Zilchas definition. We also show that there is a narrow but widely studied class of specifications in which the Zilcha test is both necessary and sufficient for dynamic inefficiency of stationary competitive equilibrium allocations. Outside this class, however, counterexamples can be constructed relatively easily.Received: 30 September 2002, Revised: 13 August 2004, JEL Classification Numbers: D51, D90, E13, E22. Correspondence to: Steven RussellWe thank Jon Burke, Subir Chakrabarti, Itzhak Zilcha and an anonymous referee for helpful conversations and/or comments.     

Corruption and the public display of wealth

We study an agent–client model of corruption, in which potential corruptors are uncertain about the probability with which officials are subjected to an audit, either high or low. We characterize a signaling equilibrium, in which officials who are less likely to be audited engage in public conspicuous consumption, whereas those who are more likely to be audited do not. In this equilibrium, officials are better off than in the equilibria without conspicuous consumption. The signaling equilibrium exists if the officials' bargaining power vis‐à‐vis potential corruptors is sufficiently high, which implies that corruption can be curbed by creating competition among officials.     

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     

Incomplete Markets, Transitory Shocks, and Welfare

Although equilibrium allocations in models with incomplete markets are generally not Pareto-efficient, it is often argued that quantitative welfare losses from missing assets are small when time horizons are long and shocks are transitory. In this paper we use a computational analysis to show that even in the simplest infinite horizon model without aggregate uncertainty welfare losses can be substantial. Furthermore we show that in this model welfare losses from incomplete markets do not necessarily disappear when one considers calibrations of the model in which agents become very patient. We argue that when the economic model is calibrated to higher frequency data, the period persistence of negative income shocks must increase as well. In this case the welfare loss of incomplete markets remains constant even as agents' rate of time preference tends to one. Journal of Economic Literature Classification Numbers: D52, D58, D60.     

Externality Policy Reform: A General Equilibrium Analysis

We characterize Pareto‐improving and equilibrium‐preserving policy reforms in a second‐best (Diamond/Mirrlees) world with a consumption externality. A counterintuitive finding is that, starting from an initial equilibrium with no direct quantity control on the externality, it is possible that all Pareto‐improving and equilibrium‐preserving directions of change require an increase in a negative externality. We provide intuition for these results by establishing a nexus between Guesnerie's approach to designing (tax) policy reforms and the standard Kuhn–Tucker technique for identifying the manifold of feasible Pareto‐optimal states, given the instruments available to the policy maker.     

A Theory of Endogenous Commitment

Commitment is typically modelled by assigning to one of the players the ability to take an initial binding action. The weakness of this approach is that the fundamental question of who has the opportunity to commit cannot be addressed, as it is assumed. This paper presents a framework in which commitment power arises endogenously from the fundamentals of the model. We construct a finite dynamic game in which players are given the option to change their minds as often as they wish, but pay a switching cost if they do so. We show that for games with two players and two actions there is a unique subgame-perfect equilibrium with a simple structure. This equilibrium is independent of the order and timing of moves and is robust to other protocol specifications. Moreover, despite the perfect information nature of the model and the costly switches, strategic delays may arise in equilibrium. The flexibility of the model allows us to apply it to various environments. In particular, we study an entry deterrence situation. Its equilibrium is intuitive and illustrative of how commitment power is endogenously determined.     

Program equilibrium

In a computerized setting, players' strategies can be implemented by computer programs, to be executed on a shared computational devise. This situation becomes typical to new Internet economies, where agent technologies play a major role. This allows the definition of a program equilibrium. Following the fundamental ideas introduced by von Neumann in the 1940s (in parallel to his seminal contribution to game theory), a computer program can be used both as a set of instructions, as well as a file that can be read and compared with other files. We show that this idea implies that in a program equilibrium of the one-shot prisoners dilemma mutual cooperation is obtained. More generally, we show that the set of program equilibrium payoffs of a game coincides with the set of feasible and individually rational payoffs of it.