On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
The limit distribution of pure strategy Nash equilibria in symmetric bimatrix games
Mathematics of Operations Research
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
The complexity of computing a Nash equilibrium
Communications of the ACM - Inspiring Women in Computing
Complexity of rational and irrational Nash equilibria
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Minimizing expectation plus variance
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Risk sensitivity of price of anarchy under uncertainty
Proceedings of the fourteenth ACM conference on Electronic commerce
Complexity of Rational and Irrational Nash Equilibria
Theory of Computing Systems
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Much of Game Theory, including the Nash equilibrium concept, is based on the assumption that players are expectation maximizers. It is known that if players are risk averse, games may no longer have Nash equilibria ([11,6]. We show that 1. Under risk aversion (convex risk valuations), and for almost all games, there are no mixed Nash equilibria, and thus either there is a pure equilibrium or there are no equilibria at all, and, 2. For a variety of important valuations other than expectation, it is NP-complete to determine if games between such players have a Nash equilibrium.