Approximating Nash Equilibria in Tree Polymatrix Games
نویسندگان
چکیده
We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for computing approximate Nash equilibria of tree polymatrix games in which the number of actions per player is a fixed constant. Further, for trees with constant degree, the running time of the algorithm matches the best known upper bound for approximating Nash equilibria in bimatrix games (Lipton, Markakis, and Mehta 2003). Notably, this work closely complements the hardness result of Rubinstein (2015), which establishes the inapproximability of Nash equilibria in polymatrix games over constant-degree bipartite graphs with two actions per player.
منابع مشابه
Tractable Algorithms for Approximate Nash Equilibria in Generalized Graphical Games with Tree Structure
We provide the first fully polynomial time approximation scheme (FPTAS) for computing an approximate mixedstrategy Nash equilibrium in graphical multi-hypermatrix games (GMhGs), which are generalizations of normal-form games, graphical games, graphical polymatrix games, and hypergraphical games. Computing an exact mixed-strategy Nash equilibria in graphical polymatrix games is PPADcomplete and ...
متن کاملFPTAS for Mixed-Strategy Nash Equilibria in Tree Graphical Games and Their Generalizations
We provide the first fully polynomial time approximation scheme (FPTAS) for computing an approximate mixed-strategy Nash equilibrium in tree-structured graphical multi-hypermatrix games (GMhGs). GMhGs are generalizations of normal-form games, graphical games, graphical polymatrix games, and hypergraphical games. Computing an exact mixed-strategy Nash equilibria in graphical polymatrix games is ...
متن کاملComputing Constrained Approximate Equilibria in Polymatrix Games
This paper is about computing constrained approximate Nash equilibria in polymatrix games, which are succinctly represented manyplayer games defined by an interaction graph between the players. In a recent breakthrough, Rubinstein showed that there exists a small constant ǫ, such that it is PPAD-complete to find an (unconstrained) ǫ-Nash equilibrium of a polymatrix game. In the first part of th...
متن کاملZero-Sum Polymatrix Games: A Generalization of Minmax
We show that in zero-sum polymatrix games, a multiplayer generalization of two-person zerosum games, Nash equilibria can be found efficiently with linear programming. We also show that the set of coarse correlated equilibria collapses to the set of Nash equilibria. In contrast, other important properties of two-person zero-sum games are not preserved: Nash equilibrium payoffs need not be unique...
متن کاملConstrained Pure Nash Equilibria in Polymatrix Games
We study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on incoming edges from players who picked the same strategy augmented by a fixed integer bonus for picking a given strategy. These games capture the idea of coord...
متن کامل