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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. Copyright Springer-Verlag Berlin/Heidelberg 2006Repeated games, Strategies, Finite automata, Trust, Experimental economics.,

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Abstract. We propose the use of a new technique-symbolic regression-as a method for inferring the strategies that are being played by subjects in economic decisionmaking experiments. We begin by describing symbolic regression and our implementation of this technique using genetic programming. We provide a brief overview of how our algorithm works and how it can be used to uncover simple data generating functions that have the flavor of strategic rules. We then apply symbolic regression using genetic programming to experimental data from the repeated "ultimatum game." We discuss and analyze the strategies that we uncover using symbolic regression and conclude by arguing that symbolic regression techniques should at least complement standard regression analyses of experimental data. IntroductionA frequently encountered problem in the analysis of data from economic decision-making experiments is how to infer subjects' strategies from their actions. The standard solution to this inference problem is to make some assumptions about how actions might be conditioned on or related to certain strategically important variables and then conduct a regression analysis using either ordinary least squares or discrete dependent variable methods. A well-known difficulty with this approach is that the strategic specification that maps explanatory variables into actions may be severely limited by the researcher's view of how subjects ought to behave in the experimental environment. While it is possible to experiment with several different strategic specifications, this is not the common practice, and in any event, the set of specifications chosen remains limited by the imagination of the researcher.In this paper, we propose the use of a new technique-symbolic regression using genetic programming-as a means of inferring the strategies that are being played by subjects in economic decision-making experiments. In contrast to standard regression analysis, symbolic regression involves the breeding of simple computer programs or functions that are a good fit to a given set of data. These computer programs are built up from a set of model primitives, specified by the researcher, which include logical if-then-else operations, mathematical and Boolean operators (and, or, not), numerical constants, and current and past realizations of variables relevant to the problem S.-H. Chen (ed.), Evolutionary Computation in Economics and Finance

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