TY - GEN

T1 - Hardness results for signaling in Bayesian zero-sum and network routing games

AU - Bhaskar, Umang

AU - Cheng, Yu

AU - Ko, Young Kun

AU - Swamy, Chaitanya

N1 - Publisher Copyright:
© Copyright 2016 ACM.

PY - 2016/7/21

Y1 - 2016/7/21

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84983494452&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983494452&partnerID=8YFLogxK

U2 - 10.1145/2940716.2940753

DO - 10.1145/2940716.2940753

M3 - Conference contribution

AN - SCOPUS:84983494452

T3 - EC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation

SP - 479

EP - 496

BT - EC 2016 - Proceedings of the 2016 ACM Conference on Economics and Computation

PB - Association for Computing Machinery, Inc

T2 - 17th ACM Conference on Economics and Computation, EC 2016

Y2 - 24 July 2016 through 28 July 2016

ER -