| dc.description.abstract | This thesis contains 5 chapters. Every chapter deals with the question of how information affects equilibrium behavior in strategic problems.
Chapter 1 is my job market paper "Limits of Global Games.'' It considers the impact of information on equilibrium multiplicity in two-player games of strategic complementarities. Games with strategic complementarities often exhibit multiple equilibria. In a global game, players privately observe a noisy signal of the underlying payoff matrix. As the noise diminishes, a unique equilibrium is selected in almost all binary-action games with strategic complementarities - a property known as "limit uniqueness.'' This chapter describes the limits of that approach in two-player games, as we move beyond two actions. Unlike binary-action games, limit uniqueness is not an intrinsic feature of all games with strategic complementarities. When the noise is symmetric, we demonstrate that limit uniqueness holds if and only if the payoffs exhibit a generalized ordinal potential property. Moreover, we provide an example illustrating how this condition can be easily violated.
Chapter 2 is co-authored with Olivier Gossner and is titled "Strategic Type Spaces.'' We provide a strategic foundation for information: in any given game with incomplete information we define strategic quotients as information representations that are sufficient for players to compute best-responses to other players. We prove 1/ existence and essential uniqueness of a minimal strategic quotient called the Strategic Type Space (STS) in which a type is given by an interim correlated rationalizability hierarchy together with the set of beliefs over other players' types and nature that rationalize this hierarchy 2/ that this minimal STS is a quotient of the universal type space and 3/ that the minimal STS has a recursive structure that is captured by a finite automaton.
Chapter 3 is also co-authored with Olivier Gossner and is titled "Information Design for Rationalizability.'' We study (interim correlated) rationalizability in games with incomplete information. For each given game, we show that a simple and finitely parameterized class of information structures is sufficient to generate every outcome distribution induced by general common prior information structures. In this parameterized family, players observe signals of two kinds: A finite signal and a common state with additive, idiosyncratic noise. We characterize the set of rationalizable outcomes of a given game as a convex polyhedron.
Chapter 4 is co-authored with Stephen Morris and Dirk Bergemann and is titled "A Strategic Topology on Information Structures.'' Two information structures are said to be close if, with high probability, there is approximate common knowledge that interim beliefs are close under the two information structures. We define an "almost common knowledge topology'' reflecting this notion of closeness. We show that it is the coarsest topology generating continuity of equilibrium outcomes. We show that finite information structures are dense in the almost common knowledge topology and thus it is without loss to restrict attention to finite information structures in information
design problems.
Finally, chapter 5 is a short note describing an information aggregation mechanism that can be used by players before playing a game of strategic complementarities under incomplete information. In such a game, players may have an incentive to share overly optimistic information with other players, thus inducing them to play higher actions. In this mechanism, players trade a token before playing the game. Players who want to communicate good news must purchase this worthless token and burn resources. The note shows that players only need to observe the market clearing price that arises from the token trades to aggregate their private information. Each element in a player's private information set is encoded as a prime in the prime factorization of the market clearing price. The element that is contained in every player's information set is identified as the prime with the highest multiplicity.
JEL Classification Codes: C72, D82 | |
