Computing Nash Equilibria of Action-Graph Games

TL;DR

This paper introduces algorithms for efficiently computing Nash equilibria in action-graph games, leveraging the game's structure to achieve exponential speedups and polynomial time in specific cases.

Contribution

It presents novel continuation algorithms for AGGs and analyzes their computational complexity, providing exponential speedups over previous methods.

Findings

Exponential speedup in computing the Jacobian of the payoff function.

Polynomial time computation when the graph's indegree is bounded and the game is symmetric.

Efficient algorithms for both symmetric and arbitrary equilibria in AGGs.

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.