Incentives, Information, and Dynamic Games: Applications in Corporations and Schools

This dissertation contains two chapters on the application of dynamics games in delegation and in school admission. The first chapter extends the standard delegation model to a two-period setting where the bias of the agent is unknown. We formalize the intuition that discretion encourages learning in the sense that the principal is more likely to learn the bias of the agent if she delegates more actions. Moreover we analyze environments in which it is optimal for the principal to induce full separation and learn the bias with probability one. In this case, the optimal delegation set, as a function of belief, is larger in the first period than that in the second period. This implies that a dynamic interaction facilitates more discretion than an one-shot relation.

The second chapter studies dynamic school admission when exploding offers are available. In the two-period game, schools can choose when to send out offers and offers are exploding in the sense that students have to respond within the period. When the quality of the students is not perfectly known by the schools, we show that there exists an equilibrium in which schools send out offers at different times. Specifically, the less competitive school tends to send out offers earlier than their more competitive counterpart. This is because the high quality students are more likely to reject early offers from the less desirable school and remain in the market hence the more competitive school can benefitby waiting. Our model provides a novel framework for the dynamic school admission problem and a new angel for understanding the usage of exploding offers on markets.