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Invariance properties of persistent equilibria and related solution concepts

  • Balkenborg, Dieter
  • Jansen, Mathijs
  • Vermeulen, Dries

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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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 41 (2001)
Issue (Month): 1 (January)
Pages: 111-130

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Handle: RePEc:eee:matsoc:v:41:y:2001:i:1:p:111-130
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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  4. C. Sanchirico, 2010. "A Probabilistic Model of Learning in Games," Levine's Working Paper Archive 484, David K. Levine.
  5. 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.
  6. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
  7. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  8. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  9. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer, vol. 32(3), pages 387-430, 06.
  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. 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).
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