Essays in Robust Mechanism Design

Abstract

Each of the three chapters of my dissertation Essays in Robust Mechanism Design belong to a developing subfield of mechanism design that seeks to provide foundations for simple and intuitive mechanisms that perform well in a wide variety of settings. In particular, my work seeks to identify contracts and mechanisms that exhibit robustness to large-scale uncertainty about agent preferences. My job market paper A Revealed Preference Approach to Multidimensional Screening develops a model of data-driven multidimensional screening, with applications to multi-good monopoly pricing and the design of complex products. In this paper, the monopolist observes a population of consumers each purchase products from one or more sets of alternatives, and she uses this choice data as the basis for her beliefs about the distribution of the buyer's preferences. However, there are many distributions of preferences that rationalize the data, and the monopolist evaluates product lineups according to their worst-case payoff against this set of distributions, in the spirit of robustness. I identify circumstances under which the monopolist can do better than to simply re-create one of the product lineups in her data set, and more broadly show how the form of the optimal selling mechanism changes under various natural restrictions to the buyer's preferences. In particular, if the monopolist is uncertain about complementarity or substitutability between product attributes, I show that it is optimal for her to sell only products that are vertically but not horizontally differentiated from the products in her data set. As part of larger project studying incentives for risk-taking, the second chapter of my dissertation Robust Contracting with Uncertain Risk Preferences studies a moral hazard problem in which the principal does not know the agent's risk preferences. The agent chooses not only how much effort to exert, but also potentially from a variety of safe and risky actions. While the existing moral hazard literature has almost uniformly employed the assumption that the principal exactly knows the agent's risk preferences, I consider a principal who seeks a contract that performs well for all types of agents. I show that all such contracts are capped bonus contracts which do not reward the agent for producing output that is either very small or very large. As a special case of my model, I identify restrictions to effort costs under which binary contracts that pay the agent a base salary and reward him with a fixed bonus payment for achieving a specified output quota are optimal. In a related paper, the third chapter of my dissertation Risk Alignment considers a moral hazard problem in which the principal is slightly uncertain about the agent's risk preferences. As before, the agent chooses not only how much effort to exert, but also what sort of risks to take. The principal's payoff depends on both the output produced by the agent and on transfers, and her risk preferences generally differ from those of the agent. In the first part of the paper, I completely characterize the set of risk aligned contracts, which provide the agent with incentives to choose risks as if his goal were to maximize the principal's payoff. Very generally, all such contracts ``pay the agent in probability'', akin to the lottery mechanisms that are used by researchers in experimental economics to induce risk preferences in laboratory subjects. In the second part of the paper, I show how risk aligned contracts are worst-case optimal for the principal.