Author: Idione Meneghel

Publisher:

Published: 2013

Total Pages: 35

ISBN-13:

"The question of existence of a Nash equilibrium is one of the most important questions in game theory. This thesis aims to advance our understanding of the question in two broad directions: 1) by providing weaker sets of sufficient conditions; and 2) by introducing novel techniques, which allow for straightforward proofs and results that give new economic insights. Discontinuous games: This project considers the existence problem in games in which strategy sets are compact and convex, but preferences of the players are represented by numerical functions that may not be continuous. One way to show existence of equilibrium in such games is to apply the 'better reply security' logic, introduced by Reny (1999), combined with some form of quasiconcavity of utility functions. As long as players have securing strategies that are robust to other players' small deviations, one can show that the game has an equilibrium. The novelty of the techniques used relies in combining three main ideas: 1) a local continuous selection of each player's strict upper contour set; 2) the idea of activating different players locally; and 3) a weak notion of convexity of preferences. Bayesian games: Games of incomplete information have been shown to apply to a huge variety of economic, political and other social interactions. Still, the question of existence of equilibria in such games has been largely dealt with on a case-by-case basis. That is, given a particular game with incomplete information, one has to find the equilibrium to prove that it exists. The reason is that the usual tools to prove existence (continuous and quasiconcave payoffs defined on convex and compact strategy sets) do not apply to the general framework of games with incomplete information. This project investigates sufficient conditions for the existence of pure-strategy Nash equilibrium in games of incomplete information. The assumption of nonatomicity of the distribution of types allows for an analysis that does not require convexity assumptions on action spaces and/or payoff functions"--Pages iv-v.