Essays on Dynamic Game Theory

Chapter 2 considers income-share agreements (ISAs), which recently have been gaining traction as a way for students to finance college education, marketed as a way for students to reduce the down-side risk of winding up in a low-paying job with high student debt. Because ISA payments are a fraction of the on-the-job wage, incentives for both applicant and provider are different from a traditional debt-financed job applicant on the job market. I develop a labor-search model to show how financing affects job-market outcomes such as wages, search duration, and overall utility, set within an equilibrium framework in which the terms and methods of financing are endogenous. I show that ISAs can constitute an important part of the college-financing decision for financially-disadvantaged potential college students, and can act well as a substitute for traditional debt-markets when the cost of college is neither very low nor very high.

Chapter 3 considers a continuous-time organization design problem. Each member's output is an imperfect signal of his underlying effort, and each member's utility from remaining in the organization is endogenous to other members' efforts. Monetary transfers are assumed infeasible. Incentives can be provided only through two channels: expulsion following poor performance and respite following good performance. We derive the steady state distribution of members' continuation utilities for arbitrary values of the initial and maximum continuation utilities and then optimize these values according to organizational objectives. An optimally designed organization can be implemented by associating continuation utilities with a performance-tracking reputation system.