Essays on game theory and its application to social discrimination and segregation

This dissertation consists of three chapters on game theory and its application to social segregation and discrimination.

In the first chapter, we discuss two interpretations of the Nash equilibrium and connect the remaining two chapters based on such interpretations. The first chapter also provides the motivations and the summary of Chapters 2 and 3.

In the second chapter, we consider an extension of an almost strictly competitive game in n-person extensive games by incorporating Seiten's subgame perfection. We call this extension a subgame perfect weakly-almost (SPWA) strictly competitive game, in particular, a SPW A strictly competitive game in strategic form is simply called a WA strictly competitive game. We give some general results on the structure of these classes of games. One result gives an easy way to verify almost strict competitiveness of a given extensive game. We show that a two-person weakly unilaterally competitive extensive game and a finitely repeated WA strictly competitive game are SPW A strictly competitive.

In the third chapter, we consider segregations, discriminatory behaviors, and prejudices in a recurrent situation of a game called the festival game with merrymakers. We show that segregation and discriminatory behaviors may occur in Nash equilibria in the sense that players of one ethnic group go to one festival, and, if any member of one ethnic group tries to go to a different festival, he will be treated differently only for the reason of nominal differences in ethnicities between them. One of our results states that if a player tries to enter a larger festival from a smaller one, he would be discriminated against by some people in the larger festival, but not necessarily if one goes from a larger one to a smaller one. We use the theory of stable conventions for the considerations of the entire recurrent situation and of the epistemic assumptions for each individual player. We show that the central parts of the stable conventions are captured by the Nash equilibria. Associating our results with the theory of stable conventions and the cognitive and moral views called subjectivism and retributionism, we discuss the emergence of fallacious views of each player about the utility functions of all the players. One such view explains prejudicial attitudes as a rationalization of discriminatory behaviors.