Designing Truthful Mechanisms: A study of Voting and Matching Rules

Abstract

Mechanisms are formal procedures used in game theory and economics to aggregate individual preferences into collective outcomes in strategic settings with private information. A truthful or strategy-proof mechanism ensures that agents are best off reporting their true preferences, thereby eliminating incentives for manipulation. Such mechanisms are important for achieving fairness, efficiency, and simplicity in practical applications. In environments without monetary transfers, voting and matching rules are two central classes of mechanisms. Voting rules are typically used for public decision-making, while matching rules allocate private goods among individuals. This thesis studies strategy-proof voting and matching rules under different environments and restrictions on preference domains. The thesis is divided into two parts: the first three chapters focus on voting rules, and the last three on matching rules. The first two chapters analyze voting environments where agents share common beliefs over the preference domain, with the relevant incentive notion being locally robust ordinal Bayesian incentive compatibility (LOBIC). Chapter one corrects a result from the existing literature, while chapter two introduces a model of correlated priors based on a betweenness property. Chapter three studies voting structures in environments where agents are connected through an exogenous graph. In this setting, we introduce incentive-compatible extendable voting rules and characterize them under different graph structures. The remaining chapters focus on matching theory. Under unrestricted preferences, the Top Trading Cycles (TTC) mechanism of Gale is known to be the unique rule satisfying strategy-proofness, individual rationality, and Pareto optimality. However, Bade showed that this uniqueness fails under single peaked preferences. Chapters four and five extend this line of research to broader preference domains: multiple single-peaked preferences and single peaked preferences on trees. In both chapters, we propose new algorithms satisfying strategy-proofness, individual rationality, and Pareto optimality. We further study the stronger notion of obvious strategy-proofness, introduced by Li (2017), proving non-existence results for such matching rules. Finally, chapter six presents general existence results for obviously strategy-proof matching rules within the class of individually rational and Pareto optimal rules.