A learning theory is proposed which models the influence of experience on end behavior in finite Prisoner's Dilemma supergames. The theory is compared with experimental results. In the experiment 35 subjects participated in 25 Prisoner's Dilemma supergames of ten periods each against anonymous opponents, changing from supergame to supergame. The typical behavior of experienced subjects involves cooperation until shortly before the end of the supergame. The theory explains shifts in the intended deviation period. On the basis of parameter estimates for each subject derived from the fn'st 20 supergames, successful predictions could be obtained for the last five supergames. 1.

Recent evidence highlights the importance of social norms in many economic relations. However, many of these relationships are long-term and provide repeated game incentives for performance. We experimentally investigate interaction effects of reciprocity and repeated game incentives in two treatments (one-shot and repeated) of a gift-exchange game. In both treatments we observe reciprocity, which is strengthened in the repeated game. A detailed analysis shows that in the repeated game some subjects imitate reciprocity. Thus, reciprocity and repeated game incentives reinforce each other. Observed behaviour is robust against experience. We conclude that a long-term interaction is a “reciprocity-compatible” contract enforcement device.

A traditional explanation for why sovereign governments repay debts is that they want to keep good reputations so they can easily borrow more. Bulow and Rogoff show that this argument is invalid under two conditions: (i) there is a single debt relationship, and (ii) regardless of their past actions, governments can earn the (possibly state-contingent) market rate of return by saving abroad. Bulow and Rogoff conjecture that, even under condition (ii), in more general reputation models with multiple relationships and spillover across them, reputation may support debt. This paper shows what is needed for this conjecture to be true. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the

Oligopoly has been among the first topics in experimental economics. Over half a century, some 150 papers have been published. Each individual paper was interested in demonstrating one effect, but in order to do so, experimenters had to specify many more parameters. Thus they have generated a huge body of evidence, untapped so far. This meta-analysis makes this evidence available. More than 100 of the papers lend themselves to calculating an index of collusion. The database behind this paper covers some 500 different settings. The experimental results may be normalized as a percentage of the span between the Walrasian and the Pareto outcomes. In the same way, results may be expressed as a percentage of the distance between the Nash and the Pareto outcomes. For each and every one of the parameters, these two indices make it possible to answer two questions: How far is the market outcome away from the competitive equilibrium? And how good is the Nash prediction? Most importantly, however, the meta-analysis sheds light on how features of the experimental setting interact with each other. Most main effects and many interaction effects are indeed statistically significant. I. RESEARCH QUESTION Richness can be embarrassing. Oligopoly has been among the first topics in experimental economics, from as early as 1959 (Hoggatt, 1959; Selten and Sauermann, 1959). In this time, a total of 154 experimental papers have been published. 1 Many of them report on more than one experiment, so that there is data on more than 500 different parameter constellations. 2 A

Abstract. In 1987 the first published research appeared which used the Genetic Algorithm as a means of seeking better strategies in playing the repeated Prisoner’s Dilemma. Since then the application of Genetic Algorithms to game-theoretical models has been used in many ways. To seek better strategies in historical oligopolistic interactions, to model economic learning, and to explore the support of cooperation in repeated interactions. This brief survey summarises related work and publications over the past thirteen years. It includes discussions of the use of gameplaying automata, co-evolution of strategies, adaptive learning, a comparison of evolutionary game theory and the Genetic Algorithm, the incorporation of historical data into evolutionary simulations, and the problems of economic simulations using real-world data. 1

Within the literature on non-cooperative game theory, there have been a number of algorithms which will compute Nash equilibria. This paper shows that the family of algorithms known as Markov chain Monte Carlo (MCMC) can be used to calculate Nash equilibria. MCMC is a type of Monte Carlo simulation that relies on Markov chains to ensure its regularity conditions. MCMC has been widely used throughout the statistics and optimization literature, where variants of this algorithm are known as simulated annealing. This paper shows that there is interesting connection between the trembles that underlie the functioning of this algorithm and the type of Nash refinement known as trembling hand perfection. This paper shows that it is possible to use simulated annealing to compute this refinement.

This paper applies game theoretic analysis to shed new light on the dynamics of market share within a contemporary, real life, entry deterrence situation. The study evaluates the market share where new entry has just occurred and considers the resulting interaction between prices, volume of business and cash flow. Insights are gained into the success or otherwise of Government intervention in the National Health Service (NHS) market from a business economics perspective. Qualitative and quantitative methods have been used to develop a mathematical framework for the analysis of strategic entry deterrence. Insights gained from Selten’s well known chain store game and a related model proposed by Waagstein are used to highlight the critical importance of enhancing a stock of knowledge and goodwill through strategic investment in information technology based service development. This study builds on previous work that proposed a method to evaluate the strategic investment profile that minimises the total investment required for dynamic entry deterrence. We extend current theories and develop a mathematical framework for evaluating market share through the application of findings from a qualitative case analysis of a single NHS pathology laboratory. The

Both in the field and in the lab, participants frequently cooperate, despite the fact that the situation can be modelled as a simultaneous, symmetric prisoner’s dilemma. This experiment manipulates the payoff in case both players defect, and explains the degree of cooperation by a combination of five motives: the size of gains from cooperation, expectations about cooperativeness in the population in question, the degree of risk and loss aversion, and the degree by which a participant is tempted to inflict harm on another participant if this gives her a chance for an even higher payoff. Information about these motivational forces stems from additional within subjects tests. All five factors are significant only if one controls for all the other motives, which suggests that a prisoner’s dilemma is a game jointly characterised by these five motives. The need to control for the remaining explanations seems to be the reason why earlier attempts at explaining choices in the prisoner’s dilemma with personality have not been successful.