Incentives and Computation: Combinatorial Auctions and Networks

This work studies centralized and decentralized protocol design in various computational environments. More specifically, we address the interplay between incentives and computational issues: we first describe positive results for restricted agents, we then show that the incentive constraint essentially implies computational hardness. Finally, we observe that in computerized networks the standard informational assumption might be relaxed. The emergence of scalable systems with self-interested entities such as electronic commerce platforms, multi-agent systems over the Internet and mobile wireless communication ad-hoc networks poses fundamental challenges. In all such scenarios the design of the protocol radically affects agents’ behavior. This suggests that the study of such systems should involve aspects of Game Theory. Algorithmic Mechanism Design [73] addresses the interplay of algorithmic considerations and game-theoretic considerations that stem from computing systems that involve participants with differing goals. More specifically, Algorithmic Mechanism Design deals with designing computationally efficient protocols for achieving global goals that require interaction with selfish agents. This field lies at the intersection of Economics, Game Theory and Computer Science. I: Combinatorial Auctions. A paradigmatic problem that captures many of these challenges is the design of Combinatorial Auctions. In a Combinatorial Auction a number of non-identical items are sold concurrently and bidders express complex preferences about combinations of items, as well as for single items. The applications are numerous: spectrum licenses, pollution permits, landing slots, allocation of computational resources, and online procurements. The challenges are ranging from purely representational questions of succinctly specifying the various bids, to purely algorithmic challenges of efficiently solving the resulting NP-hard allocation problems, to pure game-theoretic questions of bidders’ strategies and equilibria. To date, Vickrey-Clarke-Groves (VCG) mechanisms are the only known universal method for designing dominant-strategy mechanisms. However, these mechanisms when applied to Combinatorial Auctions are faced with computational NP-hardness, even when each bidder is severely restricted (e.g., if the bidder is interested in only one subset of items).