
The Complexity of Computational Problems about Nash Equilibria in Symmetric WinLose Games
We revisit the complexity of deciding, given a bimatrix game, whether i...
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Scheduling Games with MachineDependent Priority Lists
We consider a scheduling game in which jobs try to minimize their comple...
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The RockPaperScissors Game
RockPaperScissors (RPS), a game of cyclic dominance, is not merely a p...
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How to split the costs among travellers sharing a ride? Aligning system's optimum with users' equilibrium
How to form groups in a mobility system that offers shared rides, and ho...
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Strategic Payments in Financial Networks
In their seminal work on systemic risk in financial markets, Eisenberg a...
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M Equilibrium: A dual theory of beliefs and choices in games
We introduce a setvalued generalization of Nash equilibrium, called M e...
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Wireless Secret Sharing Game between Two Legitimate Users and an Eavesdropper
Wireless secret sharing is crucial to information security in the era of...
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Complexity Results about Nash Equilibria
Noncooperative game theory provides a normative framework for analyzing strategic interactions. However, for the toolbox to be operational, the solutions it defines will have to be computed. In this paper, we provide a single reduction that 1) demonstrates NPhardness of determining whether Nash equilibria with certain natural properties exist, and 2) demonstrates the #Phardness of counting Nash equilibria (or connected sets of Nash equilibria). We also show that 3) determining whether a purestrategy BayesNash equilibrium exists is NPhard, and that 4) determining whether a purestrategy Nash equilibrium exists in a stochastic (Markov) game is PSPACEhard even if the game is invisible (this remains NPhard if the game is finite). All of our hardness results hold even if there are only two players and the game is symmetric. Keywords: Nash equilibrium; game theory; computational complexity; noncooperative game theory; normal form game; stochastic game; Markov game; BayesNash equilibrium; multiagent systems.
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