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On the Inconsistency of Equilibrium Refinement

  • Werner Güth

Consistency and optimality together with converse consistency provide an illuminating and novel characterization of the equilibrium concept (Peleg and Tijs, 1996). But (together with non-emptiness) they preclude refinements of the equilibrium notion and selection of a unique equilibrium (Norde et al., 1996). We suggest two escape routes: By generalizing the concept of strict equilibrium we question the practical relevance of the existence requirement for refinements. To allow for equilibrium selection we suggest more complex reduced games which capture the inclinations of „players who already left“.

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Paper provided by Max Planck Institute of Economics, Strategic Interaction Group in its series Papers on Strategic Interaction with number 2002-48.

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Handle: RePEc:esi:discus:2002-48
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  1. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
  2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  3. van Damme, Eric, 1998. "On the State of the Art in Game Theory: An Interview with Robert Aumann," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 181-210, July.
  4. Norde, Henk & Potters, Jos & Reijnierse, Hans & Vermeulen, Dries, 1996. "Equilibrium Selection and Consistency," Games and Economic Behavior, Elsevier, vol. 12(2), pages 219-225, February.
  5. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  6. Kyle Bagwell, 1992. "Commitment and Observability in Games," Discussion Papers 1014, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Gueth, Werner & Kirchsteiger, Georg & Ritzberger, Klaus, 1996. "Imperfectly Observable Commitments in n-Player Games," Economics Series 35, Institute for Advanced Studies.
  8. Selten,Reinhard, . "An axiomatic theory of a risk dominance measure for bipolar games with linear incentives," Discussion Paper Serie B 252, University of Bonn, Germany.
  9. Harsanyi John C., 1995. "A New Theory of Equilibrium Selection for Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 10(2), pages 318-332, August.
  10. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
  11. Basu, K. & Weibull, J.W., 1990. "Strategy Subsets Closed Under Rational Behaviour," Papers 479, Stockholm - International Economic Studies.
  12. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, March.
  13. Dufwenberg, M. & Norde, H. & Reijnierse, H. & Tijs, S., 1998. "The Consistency Principle for Set-Valued Solutions and a New Direction for Normative Game Theory," Papers 1998-11, Uppsala - Working Paper Series.
  14. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  15. Sadanand, Asha & Sadanand, Venkatraman, 1996. "Firm Scale and the Endogenous Timing of Entry: a Choice between Commitment and Flexibility," Journal of Economic Theory, Elsevier, vol. 70(2), pages 516-530, August.
  16. Peleg, B. & Tijs, S., 1993. "The Consistency Principle for Games in Strategic Form," Papers 9306, Tilburg - Center for Economic Research.
  17. Spencer, Barbara J. & Brander, James A., 1992. "Pre-commitment and flexibility : Applications to oligopoly theory," European Economic Review, Elsevier, vol. 36(8), pages 1601-1626, December.
  18. Reinhard Selten, 1974. "Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games," Center for Mathematical Economics Working Papers 023, Center for Mathematical Economics, Bielefeld University.
  19. Thomson, A., 1989. "The Consistency Principle," RCER Working Papers 192, University of Rochester - Center for Economic Research (RCER).
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