Games and Decision Under Uncertainty

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Games and Decision Under Uncertainty

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Title: Games and Decision Under Uncertainty
Author: Iijima, Ryota
Citation: Iijima, Ryota. 2016. Games and Decision Under Uncertainty. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.
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Abstract: This dissertation presents three independent essays in microeconomic theory.

Chapter 1 (co-authored with Akitada Kasahara) studies the implications of gradual adjustment in strategic interactions, relative to the one-shot environment. That is, agents have flexible ability to adjust and monitor their actions before the deadline rather than committing to once-for-all choices. Its main implication is equilibrium uniqueness, which arises as an interaction with randomness of the outcome process. In the model, players take frequent and costly actions to affect the stochastic evolution of state variables that are commonly observable before the deadline. The values of these state variables influence players' terminal payoffs as well as their flow payoffs. In contrast to the one-shot case, the equilibrium is unique under a large class of terminal payoffs. We also examine the welfare implications of such gradualness in applications, including team production, hold-up problems, and dynamic contests.

Perturbed utility functions---the sum of expected utility and a non-linear perturbation function---provide a simple and tractable way to model various sorts of stochastic choice. Chapter 2 (co-authored with Drew Fudenberg and Tomasz Strzalecki) provides two easily understood conditions each of which characterizes this representation: One condition generalizes the acyclicity condition used in revealed preference theory, and the other generalizes Luce's IIA condition. We relate the discrimination or selectivity of choice rules to properties of their associated perturbations, both across different agents and across decision problems. We also show that these representations correspond to a form of ambiguity-averse preferences for an agent who is uncertain about her true utility.

Chapter 3 offers an equilibrium characterization of a general class of global games with strategic complementarities.

The analysis highlights a form of acyclicity in the interim belief structure of global games, which allows us to formalize a selection criterion, {\it iterated generalized half-dominance}. This criterion is shown to be a unique global game selection when noise distributions satisfy a regularity condition. A similar logic also applies to the perfect foresight dynamics of Matsui and Matsuyama (1995); an iterated generalized half-dominant equilibrium is a unique globally stable state when agents are patient enough.

The criterion is especially useful for games with more than two asymmetric players, and can be easily applied to local interaction games with an arbitrary network structure.
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