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The simple geometry of perfect information games

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Author Info

  • 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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File URL: http://hdl.handle.net/10.1007/s001820400169
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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. 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.
  2. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  3. repec:fth:louvco:0059 is not listed on IDEAS
  4. G. Noldeke & L. Samuelson, 2010. "An Evolutionary Analysis of Backward and Forward Induction," Levine's Working Paper Archive 538, David K. Levine.
  5. 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.
  6. R. Cressman & K.H. Schlag, . "The Dynamic (In)Stability of Backwards Induction," ELSE working papers 027, ESRC Centre on Economics Learning and Social Evolution.
  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. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
  9. Mertens, J.-F., 1988. "Stable equilibria - a reformulation," CORE Discussion Papers 1988038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. 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.
  11. van Damme,Eric, 1987. "Stable equilibria and forward induction," Discussion Paper Serie A 128, University of Bonn, Germany.
  12. 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).
  13. J. Swinkels, 2010. "Adjustment Dynamics and Rational Play in Games," Levine's Working Paper Archive 456, David K. Levine.
  14. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November.
  15. 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.
  16. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  17. 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.
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Citations

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Cited by:
  1. Stefano Demichelis, 2012. "Evolution towards asymptotic efficiency, preliminary version," Quaderni di Dipartimento 173, University of Pavia, Department of Economics and Quantitative Methods.
  2. Wladimir Raymond & Pierre Mohnen & Franz Palm & Sybrand Schim van der Loeff, 2006. "Persistence of Innovation in Dutch Manufacturing: Is it Spurious?," CIRANO Working Papers 2006s-04, CIRANO.
  3. Predtetchinski, Arkadi, 2009. "A general structure theorem for the Nash equilibrium correspondence," Games and Economic Behavior, Elsevier, vol. 66(2), pages 950-958, July.
  4. 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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