Social decision with minimal efficiency loss: An automated mechanism design approach

We study the problem where a group of agents need to choose from a finite set of social outcomes. We assume every agent's valuation for every outcome is bounded and the bounds are public information. For our model, no mechanism simultaneously satisfies strategy-proofness, individual rationality, non-deficit, and efficiency. In light of this, we aim to design mechanisms that are strategy-proof, individually rational, non-deficit, and minimize the worst-case efficiency loss. We propose a family of mechanisms called the shifted Groves mechanisms, which are generalizations of the Groves mechanisms. We first show that if there exist mechanisms that are strategy-proof, individually rational, and non-deficit, then there exist shifted Groves mechanisms with these properties. Our main result is an Automated Mechanism Design (AMD) approach for identifying the (unique) optimal shifted Groves mechanism, which minimizes the worst-case efficiency loss among all shifted Groves mechanisms. Finally, we prove that the optimal shifted Groves mechanism is globally optimal among all deterministic mechanisms that are strategy-proof, individually rational, and non-deficit.