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Invariance properties of persistent equilibria and related solution concepts

  • Balkenborg, D.
  • Jansen, M.
  • Vermeulen, D.

Kohlberg and Mertens argued that a solution concept to a game should be invariant under the addition of deletion of an equivalent strategy and not require the use of weakly dominated strategies. In this paper we study which of these requirements are satisfied by Kalai and Samet's concepts of persistent equilibria and persistent retracts. While none of these concepts has all the invariance properties, we show that a slight rephrasing of the notion of a persisent retract leads to a notion satisfying them all.

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Paper provided by Economics Division, School of Social Sciences, University of Southampton in its series Discussion Paper Series In Economics And Econometrics with number 9806.

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Date of creation: 01 Jan 1998
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Handle: RePEc:stn:sotoec:9806
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  1. Basu, K. & Weibull, J.W., 1990. "Strategy Subsets Closed Under Rational Behaviour," Papers 479, Stockholm - International Economic Studies.
  2. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer, vol. 32(3), pages 387-430, 06.
  3. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  4. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
  5. MERTENS, Jean-François, 1990. "The "small worlds" axiom for stable equilibria," CORE Discussion Papers 1990007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  7. C. Sanchirico, 2010. "A Probabilistic Model of Learning in Games," Levine's Working Paper Archive 484, David K. Levine.
  8. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  9. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  10. Vermeulen, A. J. & Jansen, M. J. M., 2000. "Ordinality of solutions of noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 13-34, February.
  11. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
  12. Vermeulen, A. J. & Jansen, M. J. M., 1997. "On the invariance of solutions of finite games," Mathematical Social Sciences, Elsevier, vol. 33(3), pages 251-267, June.
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