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
Congestion games with failures
Proceedings of the 6th ACM conference on Electronic commerce
Computing Equilibria in Anonymous Games
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
On the impact of combinatorial structure on congestion games
Journal of the ACM (JACM)
Mathematics of Operations Research
Fast and compact: a simple class of congestion games
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Games with Congestion-Averse Utilities
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Taxed congestion games with failures
Annals of Mathematics and Artificial Intelligence
The good, the bad and the cautious: safety level cooperative games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
On the existence of pure strategy nash equilibria in integer-splittable weighted congestion games
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
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Recent results regarding games with congestion-averse utilities (or, congestion-averse games--CAGs) have shown they possess some very desirable properties. Specifically, they have pure strategy Nash equilibria, which may be found in polynomial time. However, these results were accompanied by a very limiting assumption that each player is capable of using any subset of its available set of resources. This is often unrealistic--for example, resources may have complementarities between them such that a minimal number of resources is required for any to be useful. To remove this restriction, in this paper we prove the existence and tractability of a pure strategy equilibrium for a much more general setting where each player is given a matroid over the set of resources, along with the bounds on the size of a subset of resources to be selected, and its strategy space consists of all elements of this matroid that fit in the given size range. Moreover, we show that if a player strategy space in a given CAG does not satisfy these matroid properties, then a pure strategy equilibrium need not exist, and in fact the determination of whether or not a game has such an equilibrium is NP-complete. We further prove analogous results for each of the congestion-averse conditions on utility functions, thus showing that current assumptions on strategy and utility structures in this model cannot be relaxed anymore.