Uncertainty and Complexity: Essays on Statistical Decision Theory and Behavioral Economics

This dissertation studies statistical decision making and belief formation in face of uncertainty, that is, when agents' payoffs depend on an unknown distribution. Chapter 1 introduces and analyzes an equilibrium solution concept in which players sequentially sample to resolve strategic uncertainty over their opponents' distribution of actions. Bayesian players can sample from their opponents' distribution of actions at a cost and make optimal choices given their posterior beliefs. The solution concept makes predictions on the joint distribution of players' choices, beliefs, and decision times, and generates stochastic choice through the randomness inherent to sampling, without relying on indifference or choice mistakes. It rationalizes well-known deviations from Nash equilibrium such as the own-payoff effect and I show its novel predictions relating choices, beliefs, and decision times are supported by existing data. Chapter 2 presents experimental evidence establishing that the level of incentives affects both gameplay and mean beliefs.Holding fixed the actions of the other player, it is shown that, in the context of a novel class of dominance-solvable games --- diagonal games ---, higher incentives make subjects more likely to best-respond to their beliefs. Moreover, higher incentives result in more responsive beliefs but not necessarily less biased. Incentives affect effort --- as proxied by decision time --- and that it is effort, and not incentives directly, that accounts for the changes in belief formation. The results support models where, in addition to choice mistakes, players exhibit costly attention. Chapter 3 examines the class of diagonal games that are used in Chapter 2. Diagonal games constitute a new class of two-player dominance-solvable games which constitutes a useful benchmark in the study of cognitive limitations in strategic settings, both for exploring predictions of theoretical models and for experiments. This class of finite games allows for a disciplined way to vary two features of the ...