Inferring repeated-game strategies from actions: evidence from trust game experiments

Summary. Combining a strategy model, an inference procedure and a new experimental design, we map sequences of observed actions in repeated games to unobserved strategies that reflect decision-makers’ plans. We demonstrate the method by studying two institutional settings with distinct theoretical predictions. We find that almost all strategies inferred are best responses to one of the inferred strategies of other players, and in one of the settings almost all of the inferred strategies, which include triggers to punish non-cooperators, are consistent with equilibrium strategies. By developing a method to infer unobserved repeated-game strategies from actions, we take a step toward making game theory a more applied tool, bridging a gap between theory and observed behavior.Received: 23 December 2002, Revised: 19 April 2005, JEL Classification Numbers: C72, C80, C90.The authors are indebted for discussions with Ray Battalio, David Cooper, Robin Dubin, John Duffy, Ellen Garbarino, Susan Helper, Margaret Meyer, John Miller, Jim Rebitzer, Mari Rege, Al Roth, and John Van Huyck. The authors also benefited from discussants at economic department seminars at Case Western Reserve, McMaster and McGill University, University of Pittsburgh, SUNY-Stony Brook, and Texas A&M, and participants at the 2002 European Winter Meeting of the Econometric Society. We are grateful for the financial support provided by the Department of Economics at the University of Pittsburgh and Case Western Reserve University.     

On efficiency of the ratio estimator

Summary The exact mean square error for the ratio estimator of a finite population total based on simple random sampling without replacement is shown to have an expected value less than that of the variance of the ratio estimator based on Midzuno’s scheme, under a usual super-population model.     

Progressive stress accelerated life tests under finite mixture models

In this paper, progressive stress accelerated life tests are considered when the lifetime of a product under use condition follows a finite mixture of distributions. The experiment is performed when each of the components in the mixture follows a general class of distributions which includes, among others, the Weibull, compound Weibull, power function, Gompertz and compound Gompertz distributions. It is assumed that the scale parameter of each component satisfies the inverse power low, the progressive stress is directly proportional to time and the cumulative exposure model for the effect of changing stress holds. Based on type-I censoring, the maximum likelihood estimates (MLEs) of the parameters under consideration are obtained. A special attention is paid to a mixture of two Rayleigh components. Simulation results are carried out to study the precision of the MLEs and to obtain confidence intervals for the parameters involved.     

Existence of Sparsely Supported Correlated Equilibria

We show that every N-player K ₁ × ... × K _N game possesses a correlated equilibrium with at least zero entries. In particular, the largest N-player K × ... × K games with unique fully supported correlated equilibrium are two-player games. We thank an anonymous referee for most useful comments. The first author acknowledges financial support from Spanish Ministry of Science and Technology, grant SEJ2004-03619, and in form of a Ramón y Cajal fellowship. The second author acknowledges support by the PASCAL Network of Excellence under EC grant no.506778, as well as from Spanish Ministry of Science and Technology and FEDER, grant BMF2003-03324. Both authors also acknowledge financial support from BBVA grant “Aprender a jugar.”     

Empirical Bayes analysis of log-linear models for a generalized finite stationary Markov chain

This article presents the empirical Bayes method for estimation of the transition probabilities of a generalized finite stationary Markov chain whose ith state is a multi-way contingency table. We use a log-linear model to describe the relationship between factors in each state. The prior knowledge about the main effects and interactions will be described by a conjugate prior. Following the Bayesian paradigm, the Bayes and empirical Bayes estimators relative to various loss functions are obtained. These procedures are illustrated by a real example. Finally, asymptotic normality of the empirical Bayes estimators are established.     

Stochastic uncoupled dynamics and Nash equilibrium

In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence of play (the period-by-period behavior as well as the long-run frequency) to Nash equilibria of the one-shot stage game, and present a number of possibility and impossibility results. Basically, we show that if in addition to random experimentation some recall, or memory, is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it suffices to recall the last two periods of play.     

锈蚀钢筋混凝土薄壁箱梁非线形分析

薄壁箱梁结构由于其结构轻,刚度大,在结构工程中得到了广泛的应用.钢筋锈蚀是影响混凝土结构耐久性的重要因素,为了正确评估钢筋锈蚀后构件的裂缝发展情况,本文利用大型有限元软件ANSYS通过对锈蚀钢筋混凝土薄壁箱梁的非线性分析,得到了锈蚀构件的裂缝的变化规律.     

泵站底板应力弹性地基梁法与三维静力计算对比分析

底板在泵站结构计算中占重要地位。在对长洲水利枢纽库区防护下六河泵站底板应力进行计算,分别采用弹性地基梁法、三维静力（通用软件KNSYS）计算,对应力结果进行综合分析表明,三维应力分析对边墙与底板结合处、弹性地基梁法对底板中部,与实际受力状态较为一致,为下一步结构设计优化提供依据。     

Finite lifetimes,long-term debt and the fiscal limit

The U.S. faces exponentially rising entitlement obligations. I introduce a fiscal limit—a point where higher taxes are no longer a feasible financing mechanism—into a Perpetual Youth model to examine how intergenerational redistributions of wealth, the average duration of government debt, and entitlement reform impact the consequences of explosive government transfers. Three key findings emerge: (1) Growing government transfers cause more severe and more persistent stagflation than in representative agent models that do not capture intergenerational transfers of wealth; (2) A longer average duration of government debt pushes the financing of government liabilities into the future and reduces the short-run impacts of explosive transfers; (3) The time it takes the economy to rebound from a period of growing transfers increases exponentially with the number of years it takes to pass entitlement reform.