Essays in economic theory

This dissertation consists of three essays in Economic Theory. The rst essay proposes and studies a new solution concept for games with incomplete information. In game theory, there is a basic methodological dichotomy between Harsanyi's \game-theoretic" view and Aumann's \Bayesian decision-theoretic" view of the world. We follow the game theoretic view, propose and study interim partially correlated rationalizability for games with incomplete information. We argue that the distinction between this solution concept and the interim correlated rationalizability studied by Dekel, Fudenberg and Morris (2007) is fundamental, in that the latter implicitly follows Aumann's Bayesian view. Our main result shows that two types provide the same prediction in interim partially correlated rationalizability if and only if they have the same in nite hierarchy of beliefs over conditional beliefs. We also establish an equivalence result between this solution concept and the Bayesian solution{a notion of correlated equilibrium proposed by Forges (1993).

The second essay studies the relationship between correlated equilibrium the redundancy embedded in type spaces. The Bayesian solution is a notion of correlated equilibrium proposed by Forges (1993), and hierarchies of beliefs over conditional beliefs are introduced by Ely and Peski (2006) in their study of interim rationalizability. We study the connection between the two concepts. We say that two type spaces are equivalent if they represent the same set of hierarchies of beliefs over conditional beliefs. We show that the correlation embedded in equivalent type spaces can be characterized by partially correlating devices, which send correlated signals to players in a belief invariant way. Since such correlating devices also implement the Bayesian solution, we establish that the Bayesian solution is invariant across equivalent type spaces.

The third essay studies the existence of equilibria for rst-price sealed bid auctions when bidders form a network and each bidder observes perfectly their neighbors' private valuations. Asymmetry in bidders' positions in the network creates asymmetry in bidders' knowledge. We show the existence of pure-strategy equilibrium.