Essays in game theory and institutions
Rai, Birendra Kumar
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This dissertation is a compilation of essays highlighting the usefulness of game theory in understanding socio-economic phenomena. The second chapter tries to provide a reason for the strict codes of conduct that have been imposed on unmarried girls in almost every society at some point of time in its history using tools from classical game theory. If men prefer to marry submissive women, then parents of girls will have an incentive to signal the submissiveness of their daughters in various ways in order to attract better matches. At the same time, parents will find it costlier to signal the submissiveness of girls who are not really submissive. This line of reasoning thus helps us interpret phenomena such as veiling, footbinding, and sequestration of women in general as signals of submissiveness. The third chapter attempts to rationalize some of the ad hoc rules proposed for dividing a bankrupt estate using tools from evolutionary game theory. The ad hoc rules differ from each other because of the axioms that are imposed in addition to efficiency and claims boundedness. Efficiency requires that the estate be completely divided between the claimants, and claims boundedness requires that no claimant be awarded more than her initial contribution. This dissertation tries to show that an ad hoc rule can be rationalized as the unique self-enforcing long run outcome of Young's  evolutionary bargaining model by using certain intuitive rules for the Nash demand game. In the fourth chapter I present a simple model of conflict over inputs in an economy with ill-defined property rights. Agents produce output from the land they hold, which in turn can be allocated to consumption or the production of guns. There is no agency to enforce rights over the initial land holdings, and the future holdings of land are determined using a contest success function that depends on the guns produced by both agents. I characterize the equilibria in which only one, both, and none of the agents produce guns, as a function of the total land and the inequality of initial land holdings for general forms of utility, production, cost, and contest success functions.