Essays on economic theory

Abstract

The first chapter considers team incentive schemes that are robust to nonquantifiable uncertainty about the game played by the agents. A principal designs a contract for a team of agents, each taking an unobservable action that jointly determine a stochastic contractible outcome. The game is common knowledge among the agents, but the principal only knows some of the available action profiles. Realizing that the game may be bigger than he thinks, the principal evaluates contracts based on their guaranteed performance across all games consistent with his knowledge. All parties are risk neutral and the agents are protected by limited liability. A contract is said to align the agents' interests if each agent's compensation covaries positively and linearly with the other agents' compensation.

It is shown that contracts that fail to do so are dominated by those that do, both in terms of the surplus guarantee under budget balance, and in terms of the principal's profit guarantee when he is the residual claimant. It thus suffices to base compensation on a one-dimensional aggregate even if richer outcome measures are available. The best guarantee for either objective is achieved by a contract linear in the monetary value of the outcome. This provides a foundation for practices such as team-based pay and profit-sharing in partnership. The second chapter models a ride-sharing market in a traffic network with stochastic ride demands. A monopolistic ride-sharing platform in this traffic network faces a dynamic optimization problem to maximize its per period average payoff in the long run, by choosing policies of setting trip prices, matching ride requests and relocating idle drivers to meet future potential demands.

Directly solving the dynamic optimization problem for the ridesharing platform is computationally prohibitively expensive for a traffic network with reasonably large number of locations and vehicles due to its intrinsic complexity. I provide an theoretical upper bound on the performance of dynamic policies by analyzing a related deterministic problem. Based on the optimal solution to the deterministic problem, I propose implementable heuristic policies for the original stochastic problem that yield average payoffs converging to the theoretical upper bound asymptotically. I also discuss the relative value function iteration method to solve the optimization problem for small-scale markets numerically. The third chapter examines several discrete-time versions of a dynamic moral hazard in teams problem, a continuous-time model of which has been extensively studied in the previous literature.

The way to transform the continuous-time game into a discrete-time one is not unique, and different discrete-time assumptions with the same continuous-time technology limit lead to different discrete-time equilibria. Regardless of the technology assumption, I find that two-period models can give equilibrium results quite different from that in a continuous-time model: while the continuous-time model predicts existence and uniqueness of symmetric equilibrium, its two-period versions can either have multiple symmetric equilibria or none. Also, not all equilibria in the discrete-time models share features similar to the one predicted by the continuous-time model. The subsequent study of multiple-period models with no learning sheds some light on how the equilibria evolve as the discrete-time model better approximates the continuous-time one.