Approaches to mechanism design with boundedly rational agents

Abstract

This dissertation ties together three papers on mechanism design with boundedly rational agents. These papers explore theoretically whether, and to what extent, limitations on agents' ability to strategically misrepresent their preferences can help a mechanism designer achieve outcomes that she could not achieve with perfectly rational agents. The first chapter investigates whether local incentive constraints are sufficient to logically imply full incentive-compatibility, in a variety of mechanism design settings. This can be motivated by a boundedly rational model in which agents cannot contemplate all possible misrepresentations, but can consider those that are close to their true preferences. This chapter offers a unified approach that covers both continuous and discrete type spaces, showing that in many commonly studied cases, local incentive-compatibility (suitably defined) implies full incentive-compatibility. The second chapter advances the methodology of looking quantitatively at incentives for strategic behavior, motivated by the premise that agents will be truthful if the incentive to be strategic is small enough. This chapter defines a mechanism's susceptibility to manipulation as the maximum amount of expected utility any agent can ever gain from strategic misrepresntation. This measure of susceptibility is then applied to anonymous voting rules. One set of results estimates the susceptibility of specific voting rules; an important finding is that several voting systems previously identified as resistant to manipulation are actually more susceptible than simple plurality rule, by the measure proposed here. A second set of results gives asymptotic lower bounds on susceptibility for any possible voting rule, under various combinations of efficiency, regularity, and informational conditions. These results illustrate how one can quantitatively explore the tradeoffs between susceptibility and other properties of the voting rule. The third chapter carries the methodology of the second chapter to a market environment: unit-demand, private-value double auction markets. This chapter quantitatively studies the tradeoff between inefficiency and susceptibility to manipulation, among all possible mechanisms for such markets. The main result approximately locates the possibility frontier, pinning it down within a factor that is logarithmic in the size of the market.