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Absorbent Stable Sets

Author

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  • Itzhak Gilboa
  • Dov Samet

Abstract

This paper suggests a general framework to deal with learning, dynamics and evolution in games and economic environments. In this general set-up we define a (set-valued) solution concept and prove some properties, including existence. We then discuss more specific dynamical processes and show that the general solution concept provides quite intuitive results for various contexts.

Suggested Citation

  • Itzhak Gilboa & Dov Samet, 1991. "Absorbent Stable Sets," Discussion Papers 935, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:935
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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/935.pdf
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    References listed on IDEAS

    as
    1. Gilboa, Itzhak & Matsui, Akihiko, 1992. "A model of random matching," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 185-197.
    2. Kalai, Ehud & Lehrer, Ehud, 1991. "Private-Beliefs Equilibrium," Working Papers 91-19, C.V. Starr Center for Applied Economics, New York University.
    3. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    4. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    5. Crawford, Vincent P, 1995. "Adaptive Dynamics in Coordination Games," Econometrica, Econometric Society, vol. 63(1), pages 103-143, January.
    6. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August.
    7. Canning, D., 1990. "Social Equilibrium," Papers 150, Cambridge - Risk, Information & Quantity Signals.
    8. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    9. Gilboa Itzhak & Schmeidler David, 1994. "Infinite Histories and Steady Orbits in Repeated Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 370-399, May.
    10. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    11. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
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    Cited by:

    1. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
    2. Ramon Marimon & Ellen McGrattan, 1993. "On adaptive learning in strategic games," Economics Working Papers 24, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Weibull, Jörgen W., 1992. "An Introduction to Evolutionary Game Theory," Working Paper Series 347, Research Institute of Industrial Economics.

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