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International Conference on Theory and Applications of Models of Computation

TAMC 2011: Theory and Applications of Models of Computation pp 365–376Cite as

Some Tractable Win-Lose Games

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6648))

Abstract

Finding a Nash equilibrium in a bimatrix game is PPAD-hard (Chen and Deng, 2006 [3], Chen, Deng and Teng, 2009 [6]). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and Valiant, 2005 [1]). However, there do exist polynomial time tractable classes of win-lose bimatrix games - such as, very sparse games (Codenotti, Leoncini and Resta, 2006 [8]) and planar games (Addario-Berry, Olver and Vetta, 2007 [2]).

We extend the results in the latter work to K 3,3 minor-free games and a subclass of K 5 minor-free games. Both these classes strictly contain planar games. Further, we sharpen the upper bound to unambiguous logspace UL, a small complexity class contained well within polynomial time P. Apart from these classes of games, our results also extend to a class of games that contain both K 3,3 and K 5 as minors, thereby covering a large and non-trivial class of win-lose bimatrix games. For this class, we prove an upper bound of nondeterministic logspace NL, again a small complexity class in P. Our techniques are primarily graph theoretic and use structural characterizations of the considered minor-closed families.

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References

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Author information

Authors and Affiliations

  1. Chennai Mathematical Institute, India

    Samir Datta & Nagarajan Krishnamurthy

Authors
  1. Samir Datta
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  2. Nagarajan Krishnamurthy
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Miami, 1365 Memorial Drive, 33146, Coral Gables, FL, USA

    Mitsunori Ogihara

  2. Department of Information and Communication Engineering, University of Electro-Comm, Chofugaoga 1-5-1, Chofu, 182-8585, Tokyo, Japan

    Jun Tarui

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Datta, S., Krishnamurthy, N. (2011). Some Tractable Win-Lose Games. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_36

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  • DOI: https://doi.org/10.1007/978-3-642-20877-5_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20876-8

  • Online ISBN: 978-3-642-20877-5

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