Simple strategies for large zero-sum games with applications to complexity theory
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
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
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximating nash equilibria using small-support strategies
Proceedings of the 8th ACM conference on Electronic commerce
Progress in approximate nash equilibria
Proceedings of the 8th ACM conference on Electronic commerce
Games of fixed rank: a hierarchy of bimatrix games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
New algorithms for approximate Nash equilibria in bimatrix games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
An optimization approach for approximate Nash equilibria
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Polynomial algorithms for approximating nash equilibria of bimatrix games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
A note on approximate nash equilibria
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Efficient algorithms for constant well supported approximate equilibria in bimatrix games
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
IEEE Transactions on Information Theory
Inapproximability of NP-complete variants of nash equilibrium
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On the approximation performance of fictitious play in finite games
ESA'11 Proceedings of the 19th European conference on Algorithms
Approximate nash equilibria in bimatrix games
ICCCI'11 Proceedings of the Third international conference on Computational collective intelligence: technologies and applications - Volume Part II
Parameterized two-player nash equilibrium
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Spatial spectrum access game: nash equilibria and distributed learning
Proceedings of the thirteenth ACM international symposium on Mobile Ad Hoc Networking and Computing
New results on the verification of Nash refinements for extensive-form games
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Approximate well-supported nash equilibria below two-thirds
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Dynamic Pay-Per-Action Mechanisms and Applications to Online Advertising
Operations Research
Learning equilibria of games via payoff queries
Proceedings of the fourteenth ACM conference on Electronic commerce
Differential evolution as a new method of computing nash equilibria
Transactions on Computational Collective Intelligence IX
| Hi-index | 5.29 |
In view of the intractability of finding a Nash equilibrium, it is important to understand the limits of approximation in this context. A subexponential approximation scheme is known [Richard J. Lipton, Evangelos Markakis, Aranyak Mehta, Playing large games using simple strategies, in: EC, 2003], and no approximation better than 14 is possible by any algorithm that examines equilibria involving fewer than logn strategies [Ingo Althofer, On sparse approximations to randomized strategies and convex combinations, Linear Algebra and its Applications (1994) 199]. We give a simple, linear-time algorithm examining just two strategies per player and resulting in a 12-approximate Nash equilibrium in any 2-player game. For the more demanding notion of approximately well supported Nash equilibrium due to [Constantinos Daskalakis, Paul W. Goldberg, Christos H. Papadimitriou, The complexity of computing a Nash equilibrium, SIAM Journal on Computing (in press) Preliminary version appeared in STOC (2006)] no nontrivial bound is known; we show that the problem can be reduced to the case of win-lose games (games with all utilities 0 or 1), and that an approximation of 56 is possible, contingent upon a graph-theoretic conjecture. Subsequent work extends the 14 impossibility result of Ingo Althofer's paper, as mentioned above, to 12 [Tomas Feder, Hamid Nazerzadeh, Amin Saberi, Approximating nash equilibria using small-support strategies, in: EC, 2007], making our 12-approximate Nash equilibrium algorithm optimal among the algorithms that only consider mixed strategies of sublogarithmic size support. Moreover, techniques similar to our techniques for approximately well supported Nash equilibria are used in [Spyros Kontogiannis, Paul G. Spirakis, Efficient algorithms for constant well supported approximate equilibria in bimatrix games, in: ICALP, 2007] for obtaining an efficient algorithm for 0.658-approximately well supported Nash equilibria, unconditionally.