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A decomposition algorithm for N-player games

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  • Srihari Govindan

    ()

  • Robert Wilson

    ()

Abstract

An N-player game can be approximated by adding a coordinator who interacts bilaterally with each player. The coordinator proposes strategies to the players, and his payoff is maximized when each player's optimal reply agrees with his proposal. When the feasible set of proposals is finite, a solution of an associated linear complementarity problem yields an approximate equilibrium of the original game. Computational efficiency is improved by using the vertices of Kuhn's triangulation of the players' strategy space for the coordinator's pure strategies. Computational experience is reported.

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File URL: http://hdl.handle.net/10.1007/s00199-009-0434-4
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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 42 (2010)
Issue (Month): 1 (January)
Pages: 97-117

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Handle: RePEc:spr:joecth:v:42:y:2010:i:1:p:97-117

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Related research

Keywords: Game theory; Computation; Equilibrium; Decomposition; Triangulation; C63;

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References

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  1. 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.
  2. Rahul Savani & Bernhard Stengel, 2006. "Hard-to-Solve Bimatrix Games," Econometrica, Econometric Society, vol. 74(2), pages 397-429, 03.
  3. B. Curtis Eaves, 1971. "The Linear Complementarity Problem," Management Science, INFORMS, vol. 17(9), pages 612-634, May.
  4. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759 Elsevier.
  5. 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.
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Cited by:
  1. Iryna Topolyan, 2013. "Existence of perfect equilibria: a direct proof," Economic Theory, Springer, vol. 53(3), pages 697-705, August.
  2. Bernhard Stengel, 2010. "Computation of Nash equilibria in finite games: introduction to the symposium," Economic Theory, Springer, vol. 42(1), pages 1-7, January.
  3. Govindand, Srihari & Wilson, Robert B., 2008. "Computing Equilibria of N-Player Games with Arbitrary Accuracy," Research Papers 1984, Stanford University, Graduate School of Business.

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