Coordination

Many economic games have multiple equilibria, some of which are better than others for everyone involved. Such coordination games are of special interest to economists because they raise the possibility that a group of individuals or even a whole economy might become mired in an unfavorable situation. This paper explains how to use playing cards in the classroom to implement an economic game with multiple, Pareto-ranked equilibria. Discussion can focus on policies and institutions that promote coordination on better outcomes. Use: This experiment can be used in introductory economics to teach concepts of team production and coordination and in intermediate microeconomics to teach game-theoretic concepts of Nash equilibrium and Pareto optimality. Time required: Five minutes for reading instructions, 20 minutes for decision making, and about 15 minutes for discussion. Materials: You will need one or more decks of playing cards, each deck accommodating 26 people. One copy of the instructions should be made for each person. Payment to a randomly selected individual is optional and will require about a dollar or two.     

Bayesian potentials and information structures: Team decision problems revisited

This paper proposes the use of Bayesian potential games as models of informationally decentralized organizations. Applying techniques in team decision problems by Radner (1962) , this paper characterizes Bayesian Nash equilibria in terms of Bayesian potentials and demonstrates using examples that Bayesian potentials are useful tools for studying the efficient use of information in organizations.     

Incorporating fairness in generalized games of matching pennies

We examine individual behavior in generalized games of matching pennies. We have three main findings. First, individuals cooperate in these games; that is, they systematically select strategies that lead both players to obtain higher expected payoffs than in a Nash equilibrium. Second, existing models that assume altruistic preferences do not explain the cooperative behavior in these games. Third, among the main models in the extant literature, the only one that predicts the observed behavior is the quantal response equilibrium.     

Spatial Cournot Competition among Multi-Plant Firms in a Circular City

We characterize equilibrium plant locations for a spatial multi-plant Cournot oligopoly in a circular city. Previous work demonstrates that for a two-plant duopoly, all four plants are equally spaced. We establish that the equilibrium location pattern is unique if there are two firms with an equal number of plants. In most other scenarios, multiple equilibria arise. Next, we endogenously determine both the number of plants per firm and plant locations for a duopoly. It is shown that the subgame perfect Nash equilibrium may not be unique, and for identical set-up costs, the firms may choose different numbers of plants.     

The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies

This paper considers a class of models in which rank-based payoffs are sensitive to “noise” in decision making. Examples include auctions, price competition, coordination, and location games. Observed laboratory behavior in these games is often responsive to the asymmetric costs associated with deviations from the Nash equilibrium. These payoff-asymmetry effects are incorporated in an approach that introduces noisy behavior via a logit probabilistic choice function. In the resulting logit equilibrium, behavior is characterized by a probability distribution that satisfies a “rational expectations” consistency condition: The beliefs that determine players' expected payoffs match the decision distributions that arise from applying the logit rule to those expected payoffs. We prove existence of a unique, symmetric logit equilibrium and derive comparative statics results. The paper provides a unified perspective on many recent laboratory studies of games in which Nash equilibrium predictions are inconsistent with both intuition and experimental evidence.     

Equilibrium selection under cyclical disequilibrium dynamics

The paper considers an abstract economy exhibiting strategiccomplementarity and multiple, isolated Nash equilibria. It introducesexplicit disequilibrium adjustments, which are based on a combinationof adaptive and extrapolative forecasts. In this way the locallystable equilibria are typically approached in a cyclical manner.Globally, the phenomenon of overshooting increases the likelinessof regime shifting in response to exogenous shocks. In particular,even undampened cyclical behaviour is possible after a one-timeshock. A general conclusion is that the strong propagation effectsmake the economy much more susceptible to path-dependence thanit would be under the equilibrium selection hypothesis conventionallyemployed in this framework.     

中、美汇率之争的博弈分析

经济全球化时代,两国汇率的形成是两国间博弈的结果。中国是世界上最大的发展中国家,而美国是当今世界上最大的发达国家。从博弈论角度考察,两国在汇率问题上的重复博弈能够达到一个子博弈完美那什均衡。本文对人民币和美元汇率的波动运用了博弈理论分析了双方的得益和支付,并提出了中方在汇率问题上的政策建议。     

An Experimental Study of Public Information in the Asymmetric Partnership Game

This article analyzes a laboratory experiment on the novel asymmetric partnership game with public information. In this game, two players jointly work on a project each period that only benefits one of them. The public signals are about who is likely to benefit in the future, and the main treatment variable is the informativeness of these signals. Behavior is shown to be best explained by a modification of the basin of attraction (as introduced in Dal Bó and Fréchette 2011 ) to allow for state‐dependent beliefs. The public signals impact choices in the way that this theory predicts, and ultimately there is more effort when signals are more informative. Finally, a new way to investigate strategies in these types of games is considered, and it is shown that different states are used by subjects to use partial effort strategies.     

Risk Aversion and the Winner's Curse

This article analyzes an auction in which bidders see independent components of a common prize value. The Nash equilibrium for two rational bidders is shown to be independent of risk attitudes. The information structure allows explicit calculation of an alternative equilibrium in which naive bidders do not correctly discount the value of the prize, contingent on winning, and thus they suffer the winner's curse. Subjects in a laboratory experiment clearly fall prey to the winner's curse; the data conform most closely to the predictions of the naive model. Moreover, the level of risk aversion implied by fitting the naive model is similar to an independent risk aversion measure obtained in a separate (private value) bidding exercise.     

How Large Looms the Ghost of the Past? State Dependence versus Heterogeneity in Coordination Games

In games with multiple, Pareto‐rankable equilibria and repeated play, does a history of playing an inefficient equilibrium make it harder for players to reach the efficient equilibrium? In other words, can people “get stuck” in bad equilibria? Previous studies have found support for this, but they have relied on naturally occurring variation in precedent. I implement randomized control to establish that precedent effects are important, but that naturally occurring variation exaggerates the importance of precedent. I present evidence that some of the endogeneity of naturally occurring precedents is due to variation in risk attitudes. This is because in the coordination games used, the inefficient equilibrium is associated with a safe strategy. Understanding the causal effect of precedent is important since many development problems are viewed as coordination games. Moreover, an appreciation of the way in which potential heterogeneity may interact with the policy is essential when trying to lift groups out of bad precedents.     

Conventions and institutions in coordination problems

Summary This survey article starts with a game-theory interpretation of coordination problems that occur in an economy. Three types of games are discussed in which the degree of coordination versus conflict varies. It is shown that game-theoretic techniques for equilibrium selection or securing the highest pay-off outcome do not always suffice, which raises the need for exogenous information. Norms, such as conventions and institutions, may provide this information. The emergence and persistence of norms as well as the relationship between the type of game and the type of norm are discussed. After a discussion on conventions and rationality, some notions from Institutional Economics are introduced, in which institutions are explained as a way to deal with limited and costly information. Some applications are given in the last section.The author gratefully acknowledges comments given by Simon Kuipers, Hans van Ees, Elma van de Mortel and an anonymous referee without implicating them in remaining errors.     

Nash equilibria of games when players’ preferences are quasi‐transitive

Much of game theory is founded on the assumption that individual players are endowed with preferences that can be represented by a real‐valued utility function. However, in reality human preferences are often not transitive. This is especially true for the indifference relation, which can lead an individual to make a series of choices which in their totality would be viewed by the same individual as erroneous. There is a substantial literature that raises intricate questions about individual liberty and the role of government intervention in such contexts. The aim of this paper is not to go into these ethical matters but to provide a formal structure for such analysis by characterizing games where individual preferences are quasi‐transitive. The paper identifies a set of axioms which are sufficient for the existence of Nash equilibria in such “games.”     

Mixed strategy equilibria in repeated games with one-period memory

Infinitely repeated games is the pre-dominant paradigm within which economists study long-term strategic interaction. The standard framework allows players to condition their strategies on all past actions; that is, assumes that they have unbounded memory. That is clearly a convenient simplification that is at odds with reality. In this paper we restrict attention to one-period memory and characterize all totally mixed equilibria. In particular, we focus on strongly mixed equilibria. We provide conditions that are necessary and sufficient for a game to have such an equilibrium. We further demonstrate the exact set of payoffs that can be generated by such equilibria.     

纳什均衡的行为经济学精炼——基于群体感知度的认知层次模型及其实验检验

博弈论中纳什均衡解是基于完全理性人的假设,然而越来越多的经济实验结果显示:博弈结果有时与均衡预测解相悖,有时相互一致。本文在行为经济学中经典的有限理性认知层次模型上引入群体感知度参数,使得模型对于博弈结果的解释更加合理;文中也针对具体的博弈模型分析了群体感知度在形成博弈结果中的作用机理,也设计了一个简单实验对所得结论进行了检验。     

A Note on the Endogenous Timing of Tariff Policy in the Presence of a Time Lag between Production and Trade Decisions

Using the Hamilton–Slutsky extended endogenous timing game of observable delay framework, we analyze the endogenous timing of tariff policy in the presence of a time lag between production and trade decisions. In particular, focusing on the strategic relationships between an importing country’s government and an exporting monopoly firm, we show that a natural Stackelberg situation exists in which the importing country’s government as first mover determines the tariff rate and the exporting monopoly firm as second mover determines the production level. We also find that the natural Stackelberg equilibrium is Pareto superior to both the Nash and alternative Stackelberg equilibria. This implies that commitment to an ex ante optimal tariff policy before the production decision is made is optimal for the affected parties.     

The Max‐Min Group Contest: Weakest‐link (Group) All‐Pay Auction

We investigate a group all‐pay auction in which each group's effort is represented by the minimum among the effort levels exerted by the group members and the prize is a group‐specific public good. We fully characterize the symmetric equilibria for two groups. There are four types of equilibria: the pure strategy equilibria in which all (active) players exert the same effort; the semi‐pure strategy equilibria in which the players in a group play the same pure strategy whereas those in the other group play the same mixed strategy; the nondegenerate mixed strategy equilibria with continuous support; and the nondegenerate mixed strategy equilibria with discontinuous support. We then analyze a general contest with n groups.     

International environmental agreements under different evolutionary imitation mechanisms

This paper explores how the formation and stability of international environmental agreements vary with two often adopted mechanisms: imitating-the-best-average and imitating-the-best-total rules. We first show that the possible long-run equilibria of two dynamics are the same. They are countries' full participation, no-participation, and the two equilibria combined. However, the occurring conditions of these equilibria under two dynamics may differ. Then, we prove that countries' full participation is more likely to be long-run equilibrium in international environmental agreements when imitating-the-best-average rule is adopted. Moreover, all findings of this study hold whatever the function forms of countries' abnoatement benefits and costs are, and are unaffected by the positive affine transformation of countries' total payoffs.     

游戏产业发展趋势的演化博弈分析

以单机游戏及网络游戏为主要研究对象,通过探讨电脑游戏市场的两种竞争产品,若其一具有网络效应,而另一不具网络效应时,分析游戏厂商在选择所要开发产品时的动态均衡,以此来探讨我国游戏产业的发展趋势。     

Stability and instability of the unbeatable strategy in dynamic processes

A strategy is unbeatable if it is immune to any entrant strategy of any size. This paper investigates static and dynamic properties of unbeatable strategies. We give equivalent conditions for a strategy to be unbeatable and compare it with related equilibrium concepts. An unbeatable strategy is globally stable under replicator dynamics. In contrast, an unbeatable strategy can fail to be globally stable under best response dynamics even if it is also a unique and strict Nash equilibrium.     

The Evolution of Fuzzy Rules as Strategies in Two-Player Games

This paper describes simulations using fuzzy rules that show how Nash equilibrium behavior can be achieved by boundedly rational agents in two-player games with infinite strategy spaces. That is, we show how agents using simple “rules of thumb” can achieve near-equilibrium outcomes without any overt computation of the equilibrium. This is accomplished by using a genetic algorithm to approximate repeated play. Two games of differing complexities, both with analytic solutions, are examined: a repeated linear-demand Cournot game and a contestable rent game. When fuzzy rules used only the most recent information, the games we examined converged to outcomes similar to their respective Coumot-Nash equilibrium outcomes. When fuzzy rules “remembered” play from the more distant past, we found that the games converged more slowly, if at all.