Peter Stone's Selected Publications

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A Polynomial-time Nash Equilibrium Algorithm for Repeated Games

Michael L. Littman and Peter Stone. A Polynomial-time Nash Equilibrium Algorithm for Repeated Games. Decision Support Systems, 39:55–66 , 2005.
An earlier version appeared in the proceedings of the fourth annual ACM Conference on Electronic Commerce
Official version from Decision Support Systems

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Abstract

With the increasing reliance on game theory as a foundation for auctions and electronic commerce, efficient algorithms for computing equilibria in multiplayer general-sum games are of great theoretical and practical interest. The computational complexity of finding a Nash equilibrium for a one-shot bimatrix game is a well known open problem. This paper treats a related but distinct problem, that of finding a Nash equilibrium for an average-payoff repeated bimatrix game, and presents a polynomial-time algorithm. Our approach draws on the well known ``folk theorem'' from game theory and shows how finite-state equilibrium strategies can be found efficiently and expressed succinctly.

BibTeX Entry

@article(DSS04,
        author="Michael L.~Littman and Peter Stone",
        title="A Polynomial-time {N}ash Equilibrium Algorithm for Repeated Games",
        journal="Decision Support Systems",
        year="2005",
        volume="39",
        pages="55--66 ",
        abstract={
                  With the increasing reliance on game theory as a
                  foundation for auctions and electronic commerce,
                  efficient algorithms for computing equilibria in
                  multiplayer general-sum games are of great
                  theoretical and practical interest.  The
                  computational complexity of finding a Nash
                  equilibrium for a one-shot bimatrix game is a well
                  known open problem.  This paper treats a related but
                  distinct problem, that of finding a Nash equilibrium
                  for an average-payoff repeated bimatrix game,
                  and presents a polynomial-time algorithm.  Our
                  approach draws on the well known ``folk theorem''
                  from game theory and shows how finite-state
                  equilibrium strategies can be found efficiently and
                  expressed succinctly.
        },      
        wwwnote={An earlier version appeared in the proceedings of <a
href="http://cs.gmu.edu/~menasce/ec03/ecom03cfp.html">the fourth annual ACM Conference on Electronic Commerce</a><br>Official version from <a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V8S-4DFT4HY-3&_user=10&_handle=B-WA-A-W-AA-MsSAYZW-UUA-AAUBZUDBDC-AAUAAYYADC-DZAUDBCVD-AA-U&_fmt=full&_coverDate=03%2F01%2F2005&_rdoc=6&_orig=browse&_srch=%23toc%235878%232005%23999609998%23529481!&_cdi=5878&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=64dc03ccf046c25d09f2d6f5c101164f">Decision Support Systems</a>},
        )

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