Date of Degree

5-2018

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Rohit Parikh

Committee Members

Sergei Artemov

Olympia Hadjiliadis

Melvin Fitting

Subject Categories

Epistemology | Logic and Foundations | Mathematics | Other Mathematics

Keywords

Bargaining Theory, Nash Bargaining, Epistemic Game Theory, Rationalizability, Game Theory

Abstract

Chapter 1: In 1950, John Nash proposed the Bargaining Problem, for which a solution is a function that assigns to each space of possible utility assignments a single point in the space, in some sense representing the ’fair’ deal for the agents involved. Nash provided a solution of his own, and several others have been presented since then, including a notable solution by Ehud Kalai and Meir Smorodinsky. In chapter 1, a complete account is given for the conditions under which the two solutions will coincide for two player bargaining scenarios.

Chapter 2: In the same year, Nash presented one of the fundamental solution concepts of game theory, the Nash Equilibrium. Subsequently this concept was generalized by Bernheim and Pearce to the solution concept of rationalizability. Each involves a consideration of the beliefs of the agents regarding the play of the other agents, though in many strategic situations, payoffs depend not only on the actions taken, but also some facts of the world. The main result of chapter 2 is to define rationalizability for a class of such games known as Epistemic Messaging Games.

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