Complexity Results about Nash Equilibria
Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence. Pages 765-770.
Abstract
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 NP-hardness of determining whether Nash equilibria with certain natural properties exist, and 2) demonstrates the #P-hardness of counting Nash equilibria (or connected sets of Nash equilibria). We also show that 3) determining whether a purestrategy Bayes-Nash equilibrium exists is NPhard, and that 4) determining whether a purestrategy Nash equilibrium exists in a stochastic (Markov) game is PSPAC£-hard even ifthe game is invisible (this remains NP-hard if the game is finite). All of our hardness results hold even if there are only two players and the game is symmetric.
@inproceedings{ijcai2003p111,
title = {Complexity Results about Nash Equilibria},
author = {Conitzer, Vincent and Sandholm, Tuomas},
booktitle = {Proceedings of the Eighteenth International Joint Conference on
Artificial Intelligence, {IJCAI-03}},
publisher = {International Joint Conferences on Artificial Intelligence},
editor = {Georg Gottlob},
pages = {765--770},
year = {2003},
url = {https://ijcai.org/proceedings/2003/111},
}
TY - CPAPER TI - Complexity Results about Nash Equilibria AU - Conitzer, Vincent AU - Sandholm, Tuomas T2 - Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence, IJCAI-03 PB - International Joint Conferences on Artificial Intelligence PY - 2003 SP - 765 EP - 770 UR - https://ijcai.org/proceedings/2003/111 ER -Copied
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