Three essays on game theory

by Na, Sunghyun.

This thesis consists of three essays on game theory. In the first essay we consider an endogenous formation of research joint ventures by introducing heterogeneity of the firms. When the firms are characterized by a one dimensional parameter, we show that there is a tendency towards similar firms forming a coalition under an infinite-horizon sequential-move coalition unanimity rule. When there are two types of firms in the market and the number of firms of each type is equal, we show that in equilibrium there exist two coalitions, and if the degree of heterogeneity is sufficiently large we have a complete segregation of the firms in the equilibrium coalition structure, that is, all high-type firms form one coalition and all low-type firms form the other coalition. In the second essay we consider contests in which players can form coalitions before expending their efforts. When there is one strong and two weak players, we show that the strong player never forms a coalition with a weak one in an elimination contest in which the only one who survives takes the whole prize. However, we also show that a strong-weak coalition may emerge in a coalitional bargaining in which the players can make a binding agreement on the share of their coalitional worth. In the third essay we analyze optimal contracts for teams in both static and repeated setting. When an agent’s work has a positive externality on the performance signal of his peer agent, joint performance evaluation may give the strongest incentive to work and be an optimal contract in the static setting. In the same situation, relative performance evaluation may induce the use of shirk as a punishment and be an optimal contract in the repeated setting, with a large discount factor. In both static and repeated setting, relative performance evaluation is more effective when the favorable common shock is more likely to happen. iii