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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
- 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.
- Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
- 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.
- Talman, A.J.J. & van der Laan, G. & Van der Heyden, L., 1987. "Variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using general labelling," Other publications TiSEM fbe9ae2f-e01d-4eef-944c-6, Tilburg University, School of Economics and Management.
- Ehud Kalai, 2002.
"Large Robust Games,"
1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- 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.
- Ehud Kalai, 2005.
"Partially-Specified Large Games,"
1403, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- 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.
- 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.
- Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:71:y:2011:i:1:p:141-173. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.