EQUILIBRIA IN NON-COOPERATIVE GAMES I: PERTURBATIONS BASED REFINEMENTS OF NASH EQUILIBRIUM

The concept of Nash equilibrium is widely used to analyse non-cooperative games. However, one of the problems with that concept is that many games have multiple equilibria. Recent work has concentrated on reducing or refining the set of Nash equilibria in some games. In this paper, we survey some equilibrium concepts based on perturbations of strategies that refine the set of Nash equilibria. We discuss the pros and cons of each concept and its relationship to the others by the use of numerous examples and intuition. It is hoped that this survey will enable the economist to consider the relevance of a particular equilibrium concept to a given economic model of interest. Journal of Economic Literature Classification Number: C72.     

A STATISTICAL THEORY OF EQUILIBRIUM IN GAMES*

This paper describes a statistical model of equiliobrium behaviour in games, which we call Quantal Response Equilibrium (QRE). The key feature of the equilibrium is that individuals do not always play responses to the strategies of their opponents, but play better strategies with higher probability than worse strategies. we illustrate several different applications of this approach, and establish a number of theoretical properties of this equilibrium concept. We also demonstrate an equililance between this equilibrium notion and Bayesian games derived from games of complete information with perturbed payoffs     

UNIQUENESS OF EQUILIBRIUM PAYOFFS IN FINITELY REPEATED GAMES WITH IMPERFECT MONITORING*

This paper examines when a finitely repeated game with imperfect monitoring has a unique equilibrium payoff vector. This problem is nontrivial under imperfect monitoring, because uniqueness of equilibrium (outcome) in the stage game does not extend to finitely repeated games. A (correlated) equilibrium is equilibrium minimaxing if any player's equilibrium payoff is her minimax value when the other players choose a correlated action profile from the actions played in the equilibrium. The uniqueness result holds if all stage game correlated equilibria are equilibrium minimaxing and have the same payoffs. The uniqueness result does not hold under weaker conditions.     

WELFARE IN THE NASH EQUILIBRIUM IN EXPORT TAXES UNDER BERTRAND DUOPOLY

In the Eaton and Grossman Quarterly Journal of Economics, 101 (1986), pp. 383–406 model of export taxes under Bertrand duopoly, it is shown that welfare in the Nash equilibrium in export taxes is always higher than welfare under free trade for both countries.     

AN EXPERIMENTAL STUDY OF UNCERTAINTY IN COORDINATION GAMES

Global games and Poisson games have been proposed to address equilibrium indeterminacy in Common Knowledge Coordination games. The present study investigates in a controlled setup, using as controls Common Knowledge games, whether idiosyncratic uncertainty about economic fundamentals (Global games) or uncertainty about the number of actual players (Poisson games) may influence subjects' behavior. We find that uncertainty about the number of actual players has more influence on subjects' behavior than idiosyncratic uncertainty about economic fundamentals. Furthermore, subjects' behavior under Poisson population‐size uncertainty is closer to the respective theoretical prediction than subjects' behavior under idiosyncratic uncertainty about economic fundamentals.     

CYCLICAL SHOCKS IN A MODEL OF EQUILIBRIUM UNEMPLOYMENT

The paper shows a model which displays a procyclical movement of job creation as a rational expectations equilibrium.     

STRATEGIC EQUILIBRIA IN A MODEL OF ECONOMIC GROWTH WITH INPUT INTERDEPENDENCE

Two countries face a strategic interdependence in producing intermediate goods. Producing these intermediate goods requires both domestic capital and another imported intermediate good. Individually, both economies determine a balanced growth path by taking into account this interdependence in different grades of awareness. By allowing for strategic interactions in the analysis, we adapted a two‐agent dynamic setting and find an interior Markov perfect equilibrium as well as an open‐loop equilibrium reflecting these different degrees of reaction. We find that main results resemble each other but growth rates will be higher when strategies are dynamically updated.     

EQUILIBRIUM SELECTION IN THE YANO MODEL OF PRICE LEADERSHIP

Abstract. A number of studies have provided a theoretical explanation for the fact that the technologically superior firm becomes a price leader in a duopoly market for a homogeneous product. While previous studies show that the state in which the technologically superior firm becomes a price leader is a Nash equilibrium (superior leader equilibrium), they do not eliminate the possibility that the state in which the technologically inferior firm becomes a price leader is also a Nash equilibrium (inferior leader equilibrium). We demonstrate that an inferior leader equilibrium can be eliminated by the iterative elimination of weakly dominated strategies.     

EQUILIBRIUM INDETERMINACY IN A MODEL OF CONSTRAINED FINANCIAL MARKETS

I present a general equilibrium model with incomplete markets in which assets pay in units of a numéraire good. In this economy, agents are constrained to negotiate the same amount of assets in different states of the world. Different from the standard result of economies with real assets, equilibrium indeterminacy can arise, depending on the structure of the financial markets. Equilibrium fails to be unique when it is not possible to transfer wealth between states in which consumers trade a pair of assets that face the same restriction.     

对偶性一般均衡分析与国际贸易理论的深化-基于迪克西特与诺曼著《国际贸易理论》的分析

本文以迪克西特与诺曼合著的《国际贸易理论》一书为参照,分析了现代贸易理论所面临的三种挑战,探讨了对偶性一般均衡分析方法在应对这些实践挑战与深化国际贸易理论的比较优势,并且揭示了对偶性一般均衡分析方法由一种特殊的分析技术成长为国际贸易研究中的主流分析范式的过程与原因。     

IRREVERSIBILITY AND MONITORING IN DYNAMIC GAMES: EXPERIMENTAL EVIDENCE

This article provides experimental evidence on the impacts of irreversibility and imperfect monitoring on the efficiency and the equity of a repeated public goods game. We find that irreversibility and imperfect monitoring both lead to inefficient and unequal outcomes through different channels. Irreversibility lowers public goods contribution in earlier periods and makes the initial-period contribution gap between two players long-lasting. Imperfect monitoring hampers conditional cooperation and persistently reduces group contribution. A finite mixture estimation with conditional cooperators provides a coherent account of the treatment effects.     

对偶性一般均衡分析与国际贸易理论的深化-基于迪克西特与诺曼著《国际贸易理论》的分析

该文以迪克西特与诺曼合著的《国际贸易理论》一书为参照,分析了现代贸易理论所面临的三种挑战,探讨了对偶性一般均衡分析方法在应对这些实践挑战与深化国际贸易理论的比较优势,并且揭示了对偶性一般均衡分析方法由一种特殊的分析技术成长为国际贸易研究中的主流分析范式的过程与原因.     

THE DISTRIBUTION OF MONEY AND PRICES IN SEARCH EQUILIBRIUM*

This article considers a search‐theoretic model of monetary exchange. Agents bargain over both the amount of money and the quantity of goods to be exchanged in bilateral meetings, determining endogenously the distributions of money and of prices. I show that money is neutral if changes in the money supply are accomplished via proportional transfers. However, within the class of lump‐sum transfers, an increase of the rate of monetary expansion tends to decrease the dispersion of wealth and prices and to improve welfare when inflation is low; but when inflation is high enough, the opposite effects occur.     

MODELING THE EVOLUTION OF EXPECTATIONS AND UNCERTAINTY IN GENERAL EQUILIBRIUM

We develop methods to solve general equilibrium models in which forward‐looking agents are subject to waves of pessimism, optimism, and uncertainty that turn out to critically affect macroeconomic outcomes. Agents in the model are fully rational and conduct Bayesian learning, and they know that they do not know. Therefore, agents take into account that their beliefs will evolve according to what they will observe. This framework accommodates both gradual and abrupt changes in beliefs and allows for an analytical characterization of uncertainty. We use a prototypical Real Business Cycle model to illustrate the methods.     

IT'S ABOUT TIME: IMPLICATIONS OF THE PERIOD LENGTH IN AN EQUILIBRIUM SEARCH MODEL

Empirical evidence suggests that transitions between employment states are highly clustered around the first day of each workweek or month. I analyze the effect of this phenomenon by presenting an equilibrium search model in which the period length is a parameter determining the degree of clustering. Infinitesimally short periods result in a continuous‐time model with bilateral meetings, whereas longer time periods introduce the possibility of recall or simultaneity of job offers. In this environment, I show that the period length has a profound effect on equilibrium outcomes, including the unemployment rate, unemployment duration, and the cross‐sectional wage distribution.     

FEE VERSUS ROYALTY POLICY IN LICENSING THROUGH BARGAINING: AN APPLICATION OF THE NASH BARGAINING SOLUTION

In this paper, we consider a Cournot duopoly market in which the patent‐holding firm negotiates with its rival firm about payments for licensing a cost‐reducing innovation. Applying the Nash bargaining solution, we compare two licensing policies, a fixed fee and a royalty. Our results are as follows. Royalty licensing is better than fixed fee licensing for both firms if the innovation is not drastic. So, royalty licensing is always carried out. Moreover, though there exists a case in which consumers prefer fixed fee licensing, royalty licensing is always superior to fixed fee licensing from the social point of view.     

ON THE SUSTAINABILITY OF GOVERNMENT BORROWING IN A DYNAMIC GENERAL EQUILIBRIUM

Abstract.  This paper constructs a dynamic general equilibrium model with money in consumers' utility functions and investigates the equilibrium dynamics of government's debt. The limitation level of the government borrowing for which a dynamic equilibrium and the no Ponzi Game condition are compatible with each other is explicitly derived. The critical level depends on the long-run interest rate, primary balance, money supply etc.