Truthfulness and Stochastic Dominance with Monetary Transfers

Abstract

We consider truthfulness concepts for auctions with payments based on first- and second-order stochastic dominance. We assume bidders consider wealth in standard quasilinear form as valuation minus payments. Additionally, they are sensitive to risk in the distribution of wealth stemming from randomized mechanisms. First- and second-order stochastic dominance are well known to capture risk sensitivity, and we apply these concepts to capture truth-telling incentives for bidders. As our first main result, we provide a complete characterization of all social-choice functions over binary single-parameter domains that can be implemented by a mechanism that is truthful in first- and second-order stochastic dominance. We show that these are exactly the social-choice functions implementable by truthful-in-expectation mechanisms, and we provide a novel payment rule that guarantees stochastic dominance. As our second main result we extend the celebrated randomized metarounding approach for truthful-in-expectation mechanisms in packing domains. We design mechanisms that are truthful in first-order stochastic dominance by spending only a logarithmic factor in the approximation guarantee.