Mechanism Design with Spiteful Agents

We study a mechanism-design problem in which spiteful agents strive to not only maximize their rewards but also, contingent upon their own payoff levels, seek to lower the opponents' rewards. Assuming either anonymity or efficiency, as well as individual rationality, we prove that a non-null incentive-compatible (IC) mechanism does not exist. Employing a stricter notion for spitefulness, we characterize the optimal IC mechanism, which coincides with the complete characterization for the two-player setting. Leveraging these findings, we partially extend our analysis to a problem with multiple items and copies. Overall, these results illuminate the challenges of auctioning items in the natural presence of other-regarding preferences.

Joint with Aditya Aradhye and Eilon Solan.