Hardness results for signaling in Bayesian zero-sum and network routing games

Umang Bhaskar, Yu Cheng, Young Kun Ko, Chaitanya Swamy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

16 Scopus citations

Abstract

We study the optimization problem faced by a perfectly informed principal in a Bayesian game, who reveals information to the players about the state of nature to obtain a desirable equilibrium. This signaling problem is the natural design question motivated by uncertainty in games and has attracted much recent attention. We present new hardness results for signaling problems in (a) Bayesian two-player zero-sum games, and (b) Bayesian network routing games. For Bayesian zero-sum games, when the principal seeks to maximize the equilibrium utility of a player, we show that it is NP-hard to obtain an additive FPTAS. Our hardness proof exploits duality and the equivalence of separation and optimization in a novel way. Further, we rule out an additive PTAS assuming planted clique hardness, which states that no polynomial time algorithm can recover a planted clique from an Erdos-Rényi random graph. Complementing these, we obtain a PTAS for a structured class of zero-sum games (where obtaining an FPTAS is still NP-hard) when the payoff matrices obey a Lipschitz condition. Previous results ruled out an FPTAS assuming planted-clique hardness, and a PTAS only for implicit games with quasi-polynomial-size strategy sets. For Bayesian network routing games, wherein the principal seeks to minimize the average latency of the Nash flow, we show that it is NP-hard to obtain a (multiplicative) (4/3 - ϵ)-approximation, even for linear latency functions. This is the optimal inapproximability result for linear latencies, since we show that full revelation achieves a 4/3-approximation for linear latencies.

Original languageEnglish (US)
Title of host publicationEC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Pages479-496
Number of pages18
ISBN (Electronic)9781450339360
DOIs
StatePublished - Jul 21 2016
Event17th ACM Conference on Economics and Computation, EC 2016 - Maastricht, Netherlands
Duration: Jul 24 2016Jul 28 2016

Publication series

NameEC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation

Other

Other17th ACM Conference on Economics and Computation, EC 2016
Country/TerritoryNetherlands
CityMaastricht
Period7/24/167/28/16

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computer Science (miscellaneous)
  • Economics and Econometrics
  • Computational Mathematics

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