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Nash and Strongly Consistent Two-Player Game Forms

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  • Abdou, J

Abstract

A two-player game form is Nash-consistent if and only if it is tight (Gurvich). Therefore Nash-consistency of two-player game forms depends only on the effectivity structure. This fact is no longer true for strong consistency. In this paper we introduce a new object called the joint effectivity structure and define the exact joint effectivity set. These notions are similar though more sophisticated than the usual effectivity functions. We prove that a two-player game form is strongly consistent if and only if it is tight and jointly exact. Joint exactness is a property of the exact joint effectivity set which basically requires that the joint exact effectivity set coincides with the classical effectivity function. As a corollary we have a characterization of two-player strongly implementable social choice correspondences.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 24 (1995)
Issue (Month): 4 ()
Pages: 345-56

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Handle: RePEc:spr:jogath:v:24:y:1995:i:4:p:345-56

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Cited by:
  1. Joseph Abdou, 2009. "A Stability Index for Local Effectivity Functions," Documents de travail du Centre d'Economie de la Sorbonne 09041, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2009.
  2. Nikolai Kukushkin, 2011. "Acyclicity of improvements in finite game forms," International Journal of Game Theory, Springer, vol. 40(1), pages 147-177, February.
  3. repec:hal:journl:halshs-00331223 is not listed on IDEAS
  4. Abdou, Joseph & Keiding, Hans, 2003. "On necessary and sufficient conditions for solvability of game forms," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 243-260, December.
  5. repec:hal:journl:halshs-00389003 is not listed on IDEAS
  6. repec:hal:wpaper:halshs-00389181 is not listed on IDEAS
  7. Bezalel Peleg & Ariel D. Procaccia, 2007. "Implementation by Mediated Equilibrium," Discussion Paper Series dp463, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  8. repec:hal:wpaper:halshs-00347438 is not listed on IDEAS
  9. repec:hal:journl:halshs-00392508 is not listed on IDEAS
  10. Eyal Winter & Bezalel Peleg, 2002. "original papers : Constitutional implementation," Review of Economic Design, Springer, vol. 7(2), pages 187-204.
  11. Peleg, Bezalel & Peters, Hans & Storcken, Ton, 2002. "Nash consistent representation of constitutions: a reaction to the Gibbard paradox," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 267-287, March.
  12. Abdou, J., 2000. "Exact stability and its applications to strong solvability," Mathematical Social Sciences, Elsevier, vol. 39(3), pages 263-275, May.

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