Journal of Symbolic Computation
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
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Fixed-Parameter Tractability and Completeness I: Basic Results
SIAM Journal on Computing
Simplifying the weft hierarchy
Theoretical Computer Science - Parameterized and exact computation
Machine-based methods in parameterized complexity theory
Theoretical Computer Science
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The approximation complexity of win-lose games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Tight lower bounds for certain parameterized NP-hard problems
Information and Computation
Parameterized Complexity
Equilibrium Points in Fear of Correlated Threats
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
The computational complexity of trembling hand perfection and other equilibrium refinements
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
On the verification and computation of strong nash equilibrium
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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We consider approximating the minmax value of a multi-playergame in strategic form. Tightening recent bounds by Borgs et al.,we observe that approximating the value with a precision ofεlogn digits (for any constant ε 0) isNP-hard, where n is the size of the game. On the other hand,approximating the value with a precision of c loglogn digits (forany constant c ≥ 1) can be done inquasi-polynomial time. We consider the parameterized complexity ofthe problem, with the parameter being the number of pure strategiesk of the player for which the minmax value is computed. We showthat if there are three players, k = 2 and there areonly two possible rational payoffs, the minmax value is a rationalnumber and can be computed exactly in linear time. In the generalcase, we show that the value can be approximated with anypolynomial number of digits of accuracy in time n O(k). On theother hand, we show that minmax value approximation is W[1]-hardand hence not likely to be fixed parameter tractable. Concretely,we show that if k-Clique requires time n Ω(k) then so doesminmax value computation.