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
Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Computing Nash equilibria of action-graph games
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Computing equilibria in multi-player games
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the computational complexity of Nash equilibria for (0, 1) bimatrix games
Information Processing Letters
On the Complexity of Two-PlayerWin-Lose Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Reducibility among equilibrium problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Computing pure nash equilibria in graphical games via markov random fields
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
The computational complexity of nash equilibria in concisely represented games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Computing Nash Equilibria: Approximation and Smoothed Complexity
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
The approximation complexity of win-lose games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Games of fixed rank: a hierarchy of bimatrix games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computing Equilibria in Anonymous Games
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Discretized Multinomial Distributions and Nash Equilibria in Anonymous Games
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
A polynomial-time algorithm for action-graph games
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Computing pure Nash equilibria in symmetric action graph games
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
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
The game world is flat: the complexity of nash equilibria in succinct games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Computing pure strategy nash equilibria in compact symmetric games
Proceedings of the 11th ACM conference on Electronic commerce
Nash equilibrium in weighted concurrent timed games with reachability objectives
ICDCIT'12 Proceedings of the 8th international conference on Distributed Computing and Internet Technology
Computing nash equilibria of action-graph games via support enumeration
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Empirical analysis of plurality election equilibria
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
Hi-index | 0.00 |
In light of much recent interest in finding a model of multi-player multi-action games that allows for efficient computation of Nash equilibria yet remains as expressive as possible, we investigate the computational complexity of Nash equilibria in the recently proposed model of action-graph games (AGGs). AGGs, introduced by Bhat and Leyton-Brown, are succinct representations of games that encapsulate both local dependencies as in graphical games, and partial indifference to other agents' identities as in anonymous games, which occur in many natural settings such as financial markets. This is achieved by specifying a graph on the set of actions, so that the payoff of an agent for selecting a strategy depends only on the number of agents playing each of the neighboring strategies in the action graph. We present a simple Fully Polynomial Time Approximation Scheme for computing mixed Nash equilibria of AGGs with constant degree, constant treewidth and a constant number of agent types (but an arbitrary number of strategies), and extend this algorithm to a broader set of instances. However, the main results of this paper are negative, showing that when either of the latter conditions are relaxed the problem becomes intractable. In particular, we show that even if the action graph is a tree but the number of agent-types is unconstrained, it is NP- complete to decide the existence of a pure-strategy Nash equilibrium and PPAD-complete to compute a mixed Nash equilibrium (even an approximate one). Similarly for AGGs with a constant number of agent types but unconstrained treewidth. These hardness results suggest that, in some sense, our FPTAS is as strong a positive result as one can expect. In the broader context of trying to pin down the boundary where the equilibria of multi-player games can be computed efficiently, these results complement recent hardness results for graphical games and algorithmic results for anonymous games.