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Homotopy Methods to Compute Equilibria in Game Theory

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Author Info
Herings, P. Jean-Jacques
Peeters, Ronald (METEOR)

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Abstract

This paper presents a complete survey of the use of homotopy methods in game theory.Homotopies allow for a robust computation of game-theoretic equilibria and their refinements. Homotopies are also suitable to compute equilibria that are selected by variousselection theories. We present all relevant techniques underlying homotopy algorithms.We give detailed expositions of the Lemke-Howson algorithm and the Van den Elzen-Talman algorithm to compute Nash equilibria in 2-person games, and the Herings-Vanden Elzen, Herings-Peeters, and McKelvey-Palfrey algorithms to compute Nash equilibriain general n-person games.

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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 046.

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Date of creation: 2006
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Handle: RePEc:dgr:umamet:2006046

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Keywords: operations research and management science;

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  1. Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics 0211011, EconWPA. [Downloadable!]
  2. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent J., 2004. "Rationalizability for social environments," Games and Economic Behavior, Elsevier, vol. 49(1), pages 135-156, October. [Downloadable!] (restricted)
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  3. Ana Mauleon & Vincent Vannetelbosch, 2004. "Farsightedness and Cautiousness in Coalition Formation Games with Positive Spillovers," Theory and Decision, Springer, vol. 56(3), pages 291-324, 05. [Downloadable!]
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  5. Chwe Michael Suk-Young, 1994. "Farsighted Coalitional Stability," Journal of Economic Theory, Elsevier, vol. 63(2), pages 299-325, August. [Downloadable!] (restricted)
  6. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October. [Downloadable!] (restricted)
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  7. Frank H. Page, Jr. & Myrna H. Wooders, 2006. "Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games," Working Papers 0614, Department of Economics, Vanderbilt University. [Downloadable!]
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  8. Antoni Calvó-Armengol & Yves Zenou, 2004. "Social Networks And Crime Decisions: The Role Of Social Structure In Facilitating Delinquent Behavior," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(3), pages 939-958, 08. [Downloadable!] (restricted)
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  9. Bhaskar Dutta & Suresh Mutuswami, 1997. "Stable Networks," Tinbergen Institute Discussion Papers 97-039/1, Tinbergen Institute.
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  10. Olivier Tercieux & Vincent Vannetelbosch, 2006. "A characterization of stochastically stable networks," International Journal of Game Theory, Springer, vol. 34(3), pages 351-369, October. [Downloadable!] (restricted)
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  11. Matthew O. Jackson & Asher Wolinsky, 1995. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  12. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer, vol. 11(3), pages 603-627. [Downloadable!] (restricted)
  13. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February. [Downloadable!] (restricted)
  14. Jackson, Matthew O. & van den Nouweland, Anne, 2005. "Strongly stable networks," Games and Economic Behavior, Elsevier, vol. 51(2), pages 420-444, May. [Downloadable!] (restricted)
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  15. Watts, Alison, 2002. "Non-myopic formation of circle networks," Economics Letters, Elsevier, vol. 74(2), pages 277-282, January. [Downloadable!] (restricted)
  16. Page, Frank Jr. & Wooders, Myrna H. & Kamat, Samir, 2005. "Networks and farsighted stability," Journal of Economic Theory, Elsevier, vol. 120(2), pages 257-269, February. [Downloadable!] (restricted)
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  1. Frank H. Page, Jr. & Myrna H. Wooders, 2006. "Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games," Working Papers 0614, Department of Economics, Vanderbilt University. [Downloadable!]
    Other versions:
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