Penta, Antonio
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Publication Incomplete Information and Robustness in Strategic Environments(2010-05-17) Penta, AntonioGame theoretic modeling involves making assumptions on agents' infinite hierarchies of beliefs. These assumptions are understood to be only approximately satisfied in the actual situation. Thus, the significance of game theoretic predictions depend on robustness properties of the solution concepts adopted. Chapter 1 discusses recent results in this research area and their relations with the results obtained in the subsequent chapters. Chapter 2 explores the impact of misspecification of higher order beliefs in static environments, when arbitrary common knowledge assumptions on payoffs are relaxed. (Existing literature focuses on the extreme case in which all such assumptions are relaxed.) Chapter 3 provides a characterization of the strongest predictions, for dynamic games, that are "robust" to possible misspecifications of agents' higher order beliefs, and shows that such characterization depends on modeling assumptions that have hitherto received little attention in the literature (namely, the distinction between knowledge and certainty), raising novel questions of robustness. Chapter 4 develops a methodology to address classical questions of implementation, when agents' beliefs are unknown to the designer and their private information changes over time. The key idea is the identification of a solution concept that allows a tractable analysis of the full implementation problem: Full "robust" implementation requires that, for all models of agents' beliefs, all the perfect Bayesian equilibria of a mechanism induce outcomes consistent with the social choice function (SCF). It is shown that, for a weaker notion of equilibrium and for a general class of games, the set of all such equilibria can be computed by means of a "backwards procedure" that combines the logic of rationalizability and backward induction reasoning. It is further shown that a SCF is (partially) implementable for all models of beliefs if and only if it is ex-post incentive compatible. In environments with single crossing preferences, strict ex-post incentive compatibility and a "contraction property" are sufficient to guarantee full robust implementation in direct mechanisms. This property limits the interdependence in agents' valuations.