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The Simple Geometry of Perfect Information Games

Author

Listed:
  • Demichelis, Stefano

    (CORE)

  • Ritzberger, Klaus

    (Department of Economics and Finance, Institute for Advanced Studies)

  • Swinkels, Jeroen M.

    (John M. Olin School of Business, Washington University at St. Louis)

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.

Suggested Citation

  • Demichelis, Stefano & Ritzberger, Klaus & Swinkels, Jeroen M., 2002. "The Simple Geometry of Perfect Information Games," Economics Series 115, Institute for Advanced Studies.
  • Handle: RePEc:ihs:ihsesp:115
    as

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    File URL: http://www.ihs.ac.at/publications/eco/es-115.pdf
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    References listed on IDEAS

    as
    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    3. Jean-François Mertens, 1989. "Stable Equilibria---A Reformulation," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 575-625, November.
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    5. Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 207-236.
    6. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
    7. Swinkels Jeroen M., 1993. "Adjustment Dynamics and Rational Play in Games," Games and Economic Behavior, Elsevier, vol. 5(3), pages 455-484, July.
    8. Noldeke Georg & Samuelson Larry, 1993. "An Evolutionary Analysis of Backward and Forward Induction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 425-454, July.
    9. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
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    13. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
    14. Marx, Leslie M., 1999. "Adaptive Learning and Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 26(2), pages 253-278, January.
    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. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
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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. 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.
    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.

    More about this item

    Keywords

    Perfect information; Subgame perfection; Equilibrium correspondence;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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