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Computing Nash Equilibria of Action-Graph Games

Authors Kevin Leyton-Brown, Navin A.R. Bhat



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Kevin Leyton-Brown
Navin A.R. Bhat

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Kevin Leyton-Brown and Navin A.R. Bhat. Computing Nash Equilibria of Action-Graph Games. In Computing and Markets. Dagstuhl Seminar Proceedings, Volume 5011, pp. 1-8, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2005)
https://doi.org/10.4230/DagSemProc.05011.6

Abstract

This talk will survey two graphical models which the authors have proposed for compactly representing single-shot, finite-action games in which a large number of agents contend for scarce resources. The first model considered is Local-Effect Games (LEGs). These games often (but not always) have pure-strategy Nash equilibria. Finding a potential function is a good technique for finding such equilibria. We give a complete characterization of which LEGs have potential functions and provide the functions in each case; we also show a general case where pure-strategy equilibria exist in the absence of potential functions. Action-graph games (AGGs) are a fully expressive game representation which can compactly express both strict and context-specific independence between players' utility functions, and which generalize LEGs. We present algorithms for computing both symmetric and arbitrary equilibria of AGGs, based on a continuation method proposed by Govindan and Wilson. We analyze the worst- case cost of computing the Jacobian of the payoff function, the exponential- time bottleneck step of this algorithm, 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.
Keywords
  • compact representation of games
  • action-graph games
  • Nash equilibria

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