From query complexity to computational complexity
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The computational complexity of truthfulness in combinatorial auctions
Proceedings of the 13th ACM Conference on Electronic Commerce
Secondary spectrum auctions for symmetric and submodular bidders
Proceedings of the 13th ACM Conference on Electronic Commerce
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Simultaneous single-item auctions
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Truthful mechanism design for multidimensional covering problems
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Hi-index | 0.00 |
The design of computationally efficient and incentive compatible mechanisms that solve or approximate fundamental resource allocation problems is the main goal of algorithmic mechanism design. A central example in both theory and practice is welfare-maximization in combinatorial auctions. Recently, a randomized mechanism has been discovered for combinatorial auctions that is truthful in expectation and guarantees a (1-1/e)-approximation to the optimal social welfare when players have coverage valuations [DRY11]. This approximation ratio is the best possible even for non-truthful algorithms, assuming P does not equal NP. Given the recent sequence of negative results for combinatorial auctions under more restrictive notions of incentive compatibility, this development raises a natural question: Are truthful-in-expectation mechanisms compatible with polynomial-time approximation in a way that deterministic or universally truthful mechanisms are not? In particular, can polynomial-time truthful-in-expectation mechanisms guarantee a near-optimal approximation ratio for more general variants of combinatorial auctions? We prove that this is not the case. Specifically, the result of [DRY11] cannot be extended to combinatorial auctions with sub modular valuations in the value oracle model. (Absent strategic considerations, a (1-1/e)-approximation is still achievable in this setting.) More precisely, we prove that there is a constant \gamma0 such that there is no randomized mechanism that is truthful-in-expectation--or even approximately truthful-in-expectation--and guarantees an m^{-\gamma}-approximation to the optimal social welfare for combinatorial auctions with sub modular valuations in the value oracle model. We also prove an analogous result for the flexible combinatorial public projects (CPP) problem, where a truthful-in-expectation $(1-1/e)$-approximation for coverage valuations has been recently developed [Dughmi11]. We show that there is no truthful-in-expectation--or even approximately truthful-in-expectation--mechanism that achieves an m^{-\gamma}-approximation to the optimal social welfare for combinatorial public projects with sub modular valuations in the value oracle model. Both our results present an unexpected separation between coverage functions and sub modular functions, which does not occur for these problems without strategic considerations.