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The simple geometry of perfect information games

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  • Stefano Demichelis

    ()

  • Klaus Ritzberger

    ()

  • Jeroen M. Swinkels

    ()

Abstract

Perfect information games have a particularly simple structure of equilibria in the associated normal form. For generic such games each of the finitely many connected components of Nash equilibria is contractible. For every perfect information game there is a unique connected and contractible component of subgame perfect equilibria. Finally, the graph of the subgame perfect equilibrium correspondence, after a very mild deformation, looks like the space of perfect information extensive form games. Copyright Springer-Verlag 2004

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Bibliographic Info

Article provided by Springer in its journal International Journal of Games Theory.

Volume (Year): 32 (2004)
Issue (Month): 3 (06)
Pages: 315-338

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Handle: RePEc:spr:jogath:v:32:y:2004:i:3:p:315-338

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Related research

Keywords: Extensive form games; Perfect information; Subgame perfection;

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References

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  1. Swinkels, Jeroen M., 1992. "Evolution and strategic stability: From maynard smith to kohlberg and mertens," Journal of Economic Theory, Elsevier, vol. 57(2), pages 333-342, August.
  2. Noeldecke,Georg & Samuelson,Larry, . "An evolutionary analysis of backward and forward induction," Discussion Paper Serie B 228, University of Bonn, Germany.
  3. Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer, vol. 23(3), pages 207-36.
  4. Marx, Leslie M., 1999. "Adaptive Learning and Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 26(2), pages 253-278, January.
  5. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  6. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  7. Esther Hauk & Sjaak Hurkens, 1999. "On forward induction and evolutionary and strategic stability," Economics Working Papers 408, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 1999.
  8. J. Swinkels, 2010. "Adjustment Dynamics and Rational Play in Games," Levine's Working Paper Archive 456, David K. Levine.
  9. R. Cressman, K.H. Schlag, 1995. "The Dynamic (In)Stability of Backwards Induction," Discussion Paper Serie B 347, University of Bonn, Germany.
  10. Mertens, J.-F., 1988. "Stable equilibria - a reformulation," CORE Discussion Papers 1988038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
  12. Damme, E.E.C. van, 1989. "Stable equilibria and forward induction," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154422, Tilburg University.
  13. Damme, E.E.C. van, 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154427, Tilburg University.
  14. Sergiu Hart, 1999. "Evolutionary Dynamics and Backward Induction," Game Theory and Information 9905002, EconWPA, revised 23 Mar 2000.
  15. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
  16. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
  17. repec:fth:louvco:0059 is not listed on IDEAS
  18. DEMICHELIS, Stefano & RITZBERGER, Klaus, 2000. "From evolutionary to strategic stability," CORE Discussion Papers 2000059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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Citations

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Cited by:
  1. Predtetchinski, Arkadi, 2006. "A General Structure Theorem for the Nash Equilibrium Correspondence," Research Memorandum 010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Stefano Demichelis, 2012. "Evolution towards asymptotic efficiency, preliminary version," Quaderni di Dipartimento 173, University of Pavia, Department of Economics and Quantitative Methods.
  3. Kuzmics, Christoph, 2004. "Stochastic evolutionary stability in extensive form games of perfect information," Games and Economic Behavior, Elsevier, vol. 48(2), pages 321-336, August.

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