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On the complexity of approximating a nash equilibrium
Published 2012“…We show that computing a relative---that is, multiplicative as opposed to additive---approximate Nash equilibrium in two-player games is PPAD-complete, even for constant values of the approximation. …”
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On the complexity of Nash equilibria of action-graph games
Published 2012“…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). …”
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On minmax theorems for multiplayer games
Published 2012“…We show that finding a pure Nash equilibrium in coordination-only polymatrix games is PLS-complete; hence, computing a mixed Nash equilibrium is in PLS ∩ PPAD, but it remains open whether the problem is in P. …”
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Continuous local search
Published 2012“…We show that this class contains several well known intriguing problems which were heretofore known to lie in the intersection of PLS and PPAD but were otherwise unclassifiable: Finding fixpoints of contraction maps, the linear complementarity problem for P matrices, finding a stationary point of a low-degree polynomial objective, the simple stochastic games of Shapley and Condon, and finding a mixed Nash equilibrium in congestion, implicit congestion, and network coordination games. …”
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Connectivity and Equilibrium in Random Games
Published 2012“…Finally, when np=O(1/n) a pure Nash equilibrium exists with constant probability.…”
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