Choice, Learning, and Equilibrium

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This award funds research in game theory that develops new ways to analyze how people interact with each other in strategic settings, especially when people learn over time from the results of their actions. The PI plans six different research projects using a variety of methods; formal theory, numerical simulation, and lab experiments. The first and last projects characterize conditions under which evolutionary learning processes mean that behavior adjusts relatively quickly to a long run outcome. The second will produce and analyze a model of individual choice that is probabilistic and includes the time it takes to make a choice. The third project will examine how people decide whether to cooperate in a repeated interaction setting where they only observe their partner's intention with noise, and so can not be certain whether a failure to cooperate was intentional, and in addition people can make (possibly false) claims about whether they intended to cooperate. The fourth project will develop a new definition of equilibrium behavior in strategic situations to see what sorts of incorrect beliefs about other people's play are robust to rational learning when different people in the same role (e.g. "auditors" or "consumers") do not directly observe what other people in their own role do. The fifth project considers how people learn from experience when their beginning understanding of the world is not quite correct (eg, when people work to learn from misspecified models). The research will benefit society by developing new theories and methods that can help us better predict how people will respond to changes in government policies and business practices.The research will help develop a better understanding of human behavior in individual decisions and in interactive contexts. The research questions include the following. How can the widely-used drift-diffusion model of stochastic choice be improved to better match the observed data on the relationship between choice probability and decision time, while maintain its link to Bayesian optimization? What happens when the model is generalized to allow time-varying costs or other signal structures? What happens when people are trying to learn their optimal actions, and are prepared to tradeoff a lower current expected payoff for a more informative signal, but misperceive the information value of their actions because their model is mis-specified? What are the implications of learning with recency bias- the tendency to rely mostly on recent observations- for which Nash equilibria will be observed? When do evolutionary or learning models converge quickly enough that that their asymptotic behavior in large populations is relevant, and how does this relate to the amount of randomness in choice? When will players truthfully report their intended play when their actions are observed with error, and when will others learn to trust these cheap-talk and possibly false reports? What are the long-run implications of rational learning when players know their opponents' payoff functions and also know the sorts of observations (e.g. bids, values, etc.) that other players see but not their actual data? The project will be strengthen ties between economists and psychologists interested in either recency bias or the drift-diffusion model, and between economists and computer scientists interested in learning in games. Taking a longer term view, the proposed research may enhance our understanding of how and when reciprocal altruism leads to cooperation; this is of fundamental importance in many branches of social science and is also a key issue in evolutionary biology. Likewise, better understanding the foundations of stochastic choice is a fundamental issue in cognitive psychology and computational neuroscience.