Essays in epistemic game theory

Thesis (Ph. D.)--University of Rochester. Dept. of Economics, 2011.In this thesis, we make three achievements in the field of epistemic game theory: First, we show the existence of a universal type space where redundant types can be embedded. Type spaces with redundant types cannot be represented in the standard universal type space (Mertens and Zamir [39]). In Chapter 1, we extend the universal type space of Mertens-Zamir by introducing a payoff irrelevant parameter space C as a missing source of uncertainty on the lines of Liu [33] so that redundant types also can be represented there. In contrast to Liu, we show that the parameter space C can always be an exogenous space, and moreover C = {0, 1} is always enough. In Chapter 2, we apply this idea of extended universal type spaces in order to generalize the existing results in robust implementation (Bergemann and Morris [7]). Adopting knowledge-belief spaces (Aumann [5] and [6]), we show that robust implementation is equivalent to Bayesian implementation on one particular belief structure. This result allows us to directly apply the results about Bayesian implementation, such as Jackson [29], to obtain a characterization result of robust implementation in a more general class of environments. In Chapter 3, we show the impossibility of robust implementation. We apply the idea of Saijo [49], which is about the impossibility of Nash implementation, and show that only constant social choice functions are robustly implementable in large domains of interdependent preferences