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arXiv · 1207.4128

Computing Nash Equilibria of Action-Graph Games

Navin Bhat·Kevin Leyton-Brown
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Abstract

Action-graph games (AGGs) are a fully expressive game representation which can compactly express both strict and context-specific independence between players' utility functions. Actions are represented as nodes in a graph G, and the payoff to an agent who chose the action s depends only on the numbers of other agents who chose actions connected to s. We present algorithms for computing both symmetric and arbitrary equilibria of AGGs using a continuation method. We analyze the worst-case cost of computing the Jacobian of the payoff function, the exponential-time bottleneck step, and in all cases achieve exponential speedup. When the indegree of G is bounded by a constant and the game is symmetric, the Jacobian can be computed in polynomial time.

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Navin Bhat, Kevin Leyton-Brown. 2012-07-11. Computing Nash Equilibria of Action-Graph Games. https://arxiv.org/abs/1207.4128

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