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.     

Some rationalizability results for dynamic games

We study the relation between dynamical systems describing the equilibrium behavior in dynamic games and those resulting from (single‐player) dynamic optimization problems. More specifically, we derive conditions under which the dynamics generated by a model in one of these two classes can be rationalized by a model from the other class. We study this question under different assumptions about which fundamentals (e.g. technology, utility functions and time‐preference) should be preserved by the rationalization. One interesting result is that rationalizing the equilibrium dynamics of a symmetric dynamic game by a dynamic optimization problem that preserves the technology and the utility function requires a higher degree of impatience compared to that of the players in the game.     

Perfect foresight dynamics in binary supermodular games

The present paper considers equilibrium selection in binary supermodular games based on perfect foresight dynamics. We provide complete characterizations of absorbing and globally accessible equilibria and apply them to two subclasses of games. First, for unanimity games, it is shown that our selection criterion is not in agreement with that in terms of Nash products, and an example is presented in which two strict Nash equilibria are simultaneously globally accessible when the friction is sufficiently small. Second, a class of games with invariant diagonal are proposed and shown to generically admit an absorbing and globally accessible equilibrium for small frictions.     

Communication and Cooperation: A Methodological Study

We study the effect of communication in an experimental game where cooperation is consistent with equilibrium play. We examine two methodological questions which affect many studies of communication in games, particularly those studying the relationship between communication and cooperation in supergames. We show that making it easier for subjects to reach an agreement (by allowing more rounds of communication) does not increase cooperation with a limited message space treatment. Thus, limited message space treatments are not a good substitute for the use of chat. Making the game longer, thereby making the connection between the first period and the continuation game more obvious, also has little impact on cooperation. For both the two‐ and three‐period versions of our game we find substantial amounts of contingent play. This implies that use of a finitely repeated game, which has a number of methodological advantages, maintains the main properties of the underlying supergame.     

A Psychological Reexamination of the Bertrand Paradox

The Bertrand paradox describes a situation in which two competing firms reach an outcome where both price at marginal cost. In laboratory experiments, this equilibrium is not generally observed. Existing empirical works on Bertrand competition have found evidence for boundedly rational models. We find that such models are useful in organizing behavior in early stages of the game, but less so in later stages. We show that a new model, coarse grid Nash equilibrium, based on the assumption that subjects discretize the strategy space, explains the data better.     

Provision versus Appropriation in Symmetric and Asymmetric Social Dilemmas

Social dilemmas characterize decision environments in which individuals' exclusive pursuit of their own material self‐interest can produce inefficient allocations. Social dilemmas are most commonly studied in provision games, such as public goods games and trust games, in which the social dilemma can be manifested in foregone opportunities to create surplus. Appropriation games are sometimes used to study social dilemmas that can be manifested in destruction of surplus, as is typical in common‐pool resource extraction games. A central question is whether social dilemmas are more serious for inhibiting creation of surplus or in promoting its destruction. This question is addressed in this study with an experiment involving three pairs of payoff‐equivalent provision and appropriation games. Some game pairs are symmetric, whereas others involve asymmetric power relationships. We find that play of symmetric provision and appropriation games produces comparable efficiency. In contrast, power asymmetry leads to significantly lower efficiency in an appropriation game than in a payoff‐equivalent provision game. This outcome can be rationalized by reciprocal preference theory but not by models of unconditional social preferences.     

Focal Points and Economic Efficiency: The Role of Relative Label Salience

Coordination games represent coordination problems that arise across social science disciplines. Focal points have been found to be an effective way to solve many of these coordination problems. We experimentally analyze the efficiency‐enhancing power of focal points in 2 × 2 Pareto‐ranked coordination games. We find that the power of focal labels, when attached to the Pareto‐efficient strategy, to promote efficiency critically depends upon the alternative strategy's label salience. When the relative salience of our focal labels is considerably weaker, focal labels mostly fail to raise expected efficiency beyond the mixed‐strategy prediction. But when the relative salience of our focal labels is markedly stronger, focal labels raise expected efficiency much beyond the mixed‐strategy prediction. Furthermore, we find that the efficiency‐enhancing power of focal labels decreases as a measure of risk‐dominance increases across games.     

The Effect of Subtracting a Constant from all Payoffs in a Hawk‐Dove Game: Experimental Evidence of Loss Aversion in Strategic Behavior

Economists and psychologists have documented patterns of individual decision‐making behavior (e.g., loss aversion) whereby losses and gains are treated differently. However, there has been little evidence of such patterns in multiplayer games. I report results showing the strongest evidence I know of that this phenomenon is present in games. Experimental subjects play two hawk‐dove games that are identical up to a constant; in one, all payoffs are positive, while in the other, payoffs are negative if and only if both players choose “hawk.” Under both fixed pairs and random matching, differences between the games are substantial, significant, and consistent with loss aversion.     

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.     

The Effects of Alcohol Use on Economic Decision Making

In a controlled laboratory experiment, we study the causal effect of alcohol on economic decision making. A treatment group was given a dose of alcohol designed to target a blood alcohol concentration (BAC) of 0.08 while the BAC of those in the control group remained 0.00. We investigate the behavior of control and treatment groups in the following types of tasks: math, uncertainty, overconfidence, strategic games, food choice, anchoring, and altruism. Our results indicate that alcohol consumption has little systematic effect on economic behavior, at least for the BAC level considered. Further, there is little evidence that alcohol differentially impacts the choices of male and female subjects.     

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.     

Social Learning in Beauty‐Contest Games

We study the impact of social learning on the depth of reasoning in an experimental beauty‐contest game. Naive advice and observation of others' decisions as two forms of social learning trigger faster convergence to the equilibrium. We find that subjects who receive advice outperform uninformed subjects permanently, whereas subjects who observe others' past behavior before making their decision only have a temporary advantage over uninformed subjects. A series of control‐treatments and simulations indicate that the latter result is due to subjects failing to make the most out of observing others.     

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。     

Violent Video Games and Violent Crime

Video games are an increasingly popular leisure activity. As many best‐selling games contain hyper‐realistic violence, many researchers and policymakers have hypothesized that violent games cause violent behaviors. Laboratory experiments have found evidence suggesting that violent video games increase aggression. Before drawing policy conclusions about the effect of violent games on actual behavior, these experimental studies should be subjected to tests of external validity. Our study uses a quasi‐experimental methodology to identify the short‐run and medium‐run effects of violent game sales on violent crime using time variation in retail unit sales data of the top 30 selling video games and violent criminal offenses from both the Uniform Crime Report and the National Incident‐Based Reporting System from 2005 to 2011. We find no evidence of an increase in crime associated with video games and perhaps a decrease.     

Consumer Rationing and Cournot Outcomes: Experimental Evidence

We report the results of duopoly market experiments where firms first commit to capacities and then compete in prices. The theoretical literature pertaining to these duopoly models suggests that the way residual demand is rationed is fundamental to the character of equilibrium outcomes when capacity costs are sufficiently low. The experiments test this prediction by varying capacity cost and demand‐rationing schemes. We find that residual demand rationing does not significantly impact the capacity choices of experimental subjects, although it does affect pricing. Regardless of rationing scheme, the Cournot outcome is common with high capacity costs and rare with low capacity costs.     

区域产业集群内多企业间合作激励机制分析——以温州商会为例

运用重复博弈理论分析区域产业集群内多企业间合作形成的合作激励机制,认为能威慑到有不合作或背叛动机的企业从欺骗均衡转到合作均衡,激励企业间走向制度化合作。分析温州产业集群内的商会组织,发现集群内多个企业受理性驱使经过多次重复博弈可以有效地限制了潜在交易企业的不诚实行为,激励集群内所有企业走向制度化合作,增进企业整体利益,提升区域产业集群的竞争力。     

Social Networks in Economic History: Opportunities and Challenges

In this paper we survey the study of social networks and their application to economic history. We take the perspective of the applied researcher and focus on empirical methods, leaving out structural models and the literature on strategic network formation (games on networks). Our aim is to assist economic historians in identifying whether networks may be useful frameworks for their research agendas. We highlight the main challenges in using social network methods, namely, measurement error, data completeness, and the usual threats to identification of causal effects. We also review the burgeoning literature in economic history that applies network methods, organized along four main themes: markets, financial intermediation, politics and knowledge diffusion.     

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。     

Advances on Stackelberg open-loop and feedback strategies

In this paper, we study a familiar type of dynamic games called "common-property resource games" to establish the following results. First, the Stackelberg equilibrium may not exist in some cases, with open-loop strategies as well as with feedback strategies. Second, an explicit example is given to show that under feedback strategies, the best linear strategy on the part of the leader is inferior to a nonlinear strategy so that it is dangerous to confine our search to the Stackelberg equilibrium in the space of linear functions. Most importantly, we establish an "Implementation Lemma", which allows us to develop one methodology to obtain the Stackelberg equilibrium with feedback strategies when the equilibrium is assumed to exist.     

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.