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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., Economics

Chapter 1 introduces and axiomatizes a new class of representations for incomplete preferences called confidence models, which describe decision makers who behave as if they have probabilistic uncertainty over their true preferences, and are only willing to express a binary preference if it is sufficiently likely to hold. Confidence models provide a natural way to connect incomplete preferences with stochastic choice; this connection is characterized by a simple condition that serves to identify the behavioral content of incomplete preferences. Chapter 2 studies random choice rules over finite sets that obey regularity but potentially fail to satisfy all of the Block-Marschak inequalities. Such random choice rules can be represented by capacities on the space of preferences. The higher-order Block-Marschak inequalities are shown to be related to the degree of monotonicity that can be achieved by a capacity representation. Finally, Chapter 3 shows that failures of uniqueness for random utility representations are widespread. Uniqueness can be restored by introducing a finite state space and considering random choice over Savage acts. A representation is characterized in which acts are chosen according to the probability that they are optimal in every state., Economics

This dissertation presents three essays. The first essay, coauthored with Tomasz Strzalecki, is a classical exercise in axiomatic decision theory. We propose a simple and novel axiomatization of quasi-hyperbolic discounting, a tractable model of present bias preferences that has found many applications in economics. Our axiomatization imposes consistency restrictions directly on the intertemporal tradeoffs faced by the decision maker, without relying on auxiliary calibration devices such as lotteries. Such axiomatization is useful for experimental work since it renders the short-run and long-run discount factor elicitation independent of assumptions on the decision maker's utility function. The second essay, coauthored with Carolin Pflueger, belongs to the field of econometric theory. We develop a test for weak identification in the context of linear instrumental variables regression. The central feature of our test is its robustness to heteroskedasticity, autocorrelation, and clustering. We define identification to be weak when the Two-Stage Least Squares (TSLS) or the Limited Information Maximum Likelihood (LIML) Nagar bias is large relative to a benchmark. To test the null hypothesis of weak identification we propose a scaled non-robust first stage F statistic: the effective F. The test rejects for large values of the effective F. The critical values depend on an estimate of the covariance matrix of the OLS reduced form regression coefficients and on the covariance matrix of the reduced form errors. The third essay—the main chapter of this dissertation—belongs to the intersection of econometric theory and statistical decision theory. I present a new class of tests for hypothesis testing problems with a special feature: a boundary-sufficient statistic. The new tests minimize a weighted sum of the average rates of Type I and Type II error (average risk), while controlling the conditional rejection probability on the boundary of the null hypothesis; in this sense they are efficient conditionally similar on the boundary (ecs). The ecs tests emerge from an axiomatic approach: they essentially characterize admissibility—an important finite-sample optimality property—and similarity on the boundary in the class of all tests, provided the boundary-sufficient statistic is boundedly complete., Economics