Journal of the ACM (JACM)
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Price of Routing Unsplittable Flow
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
When selfish meets evil: byzantine players in a virus inoculation game
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
On the Impact of Combinatorial Structure on Congestion Games
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Congestion games with malicious players
Proceedings of the 8th ACM conference on Electronic commerce
Selfish Routing with Incomplete Information
Theory of Computing Systems
Complexity of pure equilibria in Bayesian games
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Total latency in singleton congestion games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
On the complexity of pure-strategy nash equilibria in congestion and local-effect games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Exact price of anarchy for polynomial congestion games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Symmetry in network congestion games: pure equilibria and anarchy cost
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
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In this paper, we introduce malicious Bayesian congestion games as an extension to congestion games where players might act in a malicious way. In such a game each player has two types . Either the player is a rational player seeking to minimize her own delay, or --- with a certain probability --- the player is malicious in which case her only goal is to disturb the other players as much as possible. We show that such games do in general not possess a Bayesian Nash equilibrium in pure strategies (i.e. a pure Bayesian Nash equilibrium ). Moreover, given a game, we show that it is NP-complete to decide whether it admits a pure Bayesian Nash equilibrium. This result even holds when resource latency functions are linear, each player is malicious with the same probability, and all strategy sets consist of singleton sets of resources. For a slightly more restricted class of malicious Bayesian congestion games, we provide easy checkable properties that are necessary and sufficient for the existence of a pure Bayesian Nash equilibrium. In the second part of the paper we study the impact of the malicious types on the overall performance of the system (i.e. the social cost ). To measure this impact, we use the Price of Malice . We provide (tight) bounds on the Price of Malice for an interesting class of malicious Bayesian congestion games. Moreover, we show that for certain congestion games the advent of malicious types can also be beneficial to the system in the sense that the social cost of the worst case equilibrium decreases. We provide a tight bound on the maximum factor by which this happens.