Essays in Robustness and Mechanism Design

Abstract

This thesis is a theoretical study of the design of optimal mechanisms and relevant robustness considerations in game theory. Chapter 1 examines contracting with moral hazard where an agent has available a known, or baseline, production technology but the principal thinks that the agent may also have access to other technologies, and maximizes her worst-case expected utilities under those possible technologies. That is, the principal aims to design a robust contract, where the level of robustness is the unknown technologies the principal thinks are possible. I show that all Pareto-efficient contracts take the form of participating preferred equity, a mixture of debt and equity. As the principal becomes more concerned with robustness the equity component of efficient contracts increases: the contracts move from debt, via participating preferred equity, to equity.

Chapter 2 (with Matias Iaryczower) studies a common feature in the design of agency relationships: that principals can decide both the direction and the scope or scale of implementation of a policy. There is a natural complementarity between these dimensions: the value of expanding the scale of implementation increases when the policy is close to a player's preferred policy. In the absence of transfers the optimal separating contract involves delegation with strings attached: an agent with an upward policy bias can only choose higher policies by reducing the scale. The solution differs qualitatively from standard quasilinear models and is ex-post inefficient, as the highest policies are too low for both parties and are under-implemented.

Chapter 3 (with Marco Battaglini) considers the robustness of inefficiency results in the literature on dynamic contribution games: a class of stochastic games where a player's action (contribution) is assumed to be monotonic. The literature finds that contributions are gradual and efficient outcomes are not achievable. In this chapter, we show that these results are not robust when some depreciation of contributions is allowed. In particular, we prove that the folk theorem holds in this setting and thus are able to support efficient levels of the public good. This has important implications for modelling public good games, as small modelling choices deliver very different outcomes.