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Action-Graph Games

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  • Jiang, Albert Xin
  • Leyton-Brown, Kevin
  • Bhat, Navin A.R.
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    Abstract

    Representing and reasoning with games becomes difficult once they involve large numbers of actions and players, because the space requirement for utility functions can grow unmanageably. Action-Graph Games (AGGs) are a fully-expressive game representation that can compactly express utility functions with structure such as context-specific independence, anonymity, and additivity. We show that AGGs can be used to compactly represent all games that are compact when represented as graphical games, symmetric games, anonymous games, congestion games, and polymatrix games, as well as games that require exponential space under all of these existing representations. We give a polynomial-time algorithm for computing a player's expected utility under an arbitrary mixed-strategy profile, and show how to use this algorithm to achieve exponential speedups of existing methods for computing sample Nash equilibria. We present results of experiments showing that using AGGs leads to a dramatic increase in the size of games accessible to computational analysis.2

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    File URL: http://www.sciencedirect.com/science/article/B6WFW-51D15XK-1/2/00b698765d4a87811129b1cc5effd5a3
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    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 71 (2011)
    Issue (Month): 1 (January)
    Pages: 141-173

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    Handle: RePEc:eee:gamebe:v:71:y:2011:i:1:p:141-173

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    Web page: http://www.elsevier.com/locate/inca/622836

    Related research

    Keywords: Game representations Graphical models Large games Computational techniques Nash equilibria;

    References

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    1. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    2. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation for Research in Economics, Yale University.
    3. Turocy, Theodore L., 2005. "A dynamic homotopy interpretation of the logistic quantal response equilibrium correspondence," Games and Economic Behavior, Elsevier, vol. 51(2), pages 243-263, May.
    4. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    5. Ehud Kalai, 2005. "Partially-Specified Large Games," Levine's Bibliography 784828000000000565, UCLA Department of Economics.
    6. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    7. Talman, A.J.J. & Laan, G. van der & Van der Heyden, L., 1987. "Variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using general labelling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153106, Tilburg University.
    8. Govindan, Srihari & Wilson, Robert, 2003. "A global Newton method to compute Nash equilibria," Journal of Economic Theory, Elsevier, vol. 110(1), pages 65-86, May.
    9. Govindan, Srihari & Wilson, Robert, 2004. "Computing Nash equilibria by iterated polymatrix approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1229-1241, April.
    10. Eli Ben-Sasson & Adam Tauman Kalai & Ehud Kalai, 2006. "An Approach to Bounded Rationality," Discussion Papers 1439, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
    12. Koller, Daphne & Milch, Brian, 2003. "Multi-agent influence diagrams for representing and solving games," Games and Economic Behavior, Elsevier, vol. 45(1), pages 181-221, October.
    13. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
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    Cited by:
    1. Berno Buechel & Nils Roehl, 2013. "Robust Equilibria in Location Games," Working Papers CIE 58, University of Paderborn, CIE Center for International Economics.
    2. repec:pdn:wpaper:58 is not listed on IDEAS

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