Self-interested automated mechanism design and implications for optimal combinatorial auctions

Often, an outcome must be chosen on the basis of the preferences reported by a group of agents. The key difficulty is that the agents may report their preferences insincerely to make the chosen outcome more favorable to themselves. Mechanism design is the art of designing the rules of the game so that the agents are motivated to report their preferences truthfully, and a desirable outcome is chosen. In a recently proposed approach---called automated mechanism design ---a mechanism is computed for the preference aggregation setting at hand. This has several advantages, but the downside is that the mechanism design optimization problem needs to be solved anew each time. Unlike the earlier work on automated mechanism design that studied a benevolent designer, in this paper we study automated mechanism design problems where the designer is self-interested. In this case, the center cares only about which outcome is chosen and what payments are made to it. The reason that the agents' preferences are relevant is that the center is constrained to making each agent at least as well off as the agent would have been had it not participated in the mechanism. In this setting, we show that designing optimal deterministic mechanisms is NP-complete in two important special cases: when the center is interested only in the payments made to it, and when payments are not possible and the center is interested only in the outcome chosen. We then show how allowing for randomization in the mechanism makes problems in this setting computationally easy. Finally, we show that the payment-maximizing AMD problem is closely related to an interesting variant of the optimal (revenue-maximizing) combinatorial auction design problem, where the bidders have "best-only" preferences. We show that here, too, designing an optimal deterministic auction is NP-complete, but designing an optimal randomized auction is easy.