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On non-cooperative foundation and implementation of the Nash Solution in subgame perfect equilibrium via Rubinstein’s game

Listed author(s):
  • Duman, Papatya

    (Center for Mathematical Economics, Bielefeld University)

  • Trockel, Walter

    (Center for Mathematical Economics, Bielefeld University)

The alternating offers game due to Rubinstein (1982) had been used by Binmore (1980) and by Binmore et.al. (1986) to provide via its unique subgame perfect equilibrium an approximate non-cooperative support for the Nash bargaining solution of associated cooperative two-person bargaining games. These results had strengthened the prominent role of the Nash bargaining solution in cooperative axiomatic bargaining theory and its application, for instance in labor markets, and have often even be interpreted as a mechanism theoretical implementation of the Nash solution. Our results in the present paper provide exact non-cooperative foundations first, in our Proposition, via weakly subgame perfect equilibria of a game that is a modification of Rubinstein´s game, then in our Theorem, via sub-game perfect equilibria of a game that is a further modification of our first game. Moreover, they provide a general rule how to transform approximate support results into exact ones. Finally, we discuss the relation of the above mentioned support results, including our present ones, with mechanism theoretic implementation in (weakly) subgame perfect equilibrium of the Nash solution. There we come to the conclusion that a sound interpretation as an implementation can hardly be found except in very rare cases of extremely restricted domains of players´ preferences.

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File URL: https://pub.uni-bielefeld.de/download/2900384/2900385
File Function: First Version, 2016
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Paper provided by Center for Mathematical Economics, Bielefeld University in its series Center for Mathematical Economics Working Papers with number 550.

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Length: 17
Date of creation: 15 Jan 2016
Handle: RePEc:bie:wpaper:550
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  1. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, vol. 55(2), pages 203-208, August.
  2. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
  3. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
  4. Leonid Hurwicz, 1994. "Economic design, adjustment processes, mechanisms, and institutions," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 1-14, December.
  5. Trockel, Walter, 2011. "An exact non-cooperative support for the sequential Raiffa solution," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 77-83, January.
  6. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  7. Dagan, Nir & Serrano, Roberto, 1998. "Invariance and randomness in the Nash program for coalitional games," Economics Letters, Elsevier, vol. 58(1), pages 43-49, January.
  8. Eric van Damme, 1984. "The Nash Bargaining Solution is Optimal," Discussion Papers 597, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Howard, J. V., 1992. "A social choice rule and its implementation in perfect equilibrium," Journal of Economic Theory, Elsevier, vol. 56(1), pages 142-159, February.
  10. Sudholter, Peter & Rosenmuller, Joachim & Peleg, Bezalel, 2000. "The canonical extensive form of a game form: Part II. Representation," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 299-338, April.
  11. Moulin, H., 1984. "Implementing the Kalai-Smorodinsky bargaining solution," Journal of Economic Theory, Elsevier, vol. 33(1), pages 32-45, June.
  12. Walter Trockel, 2002. "A universal meta bargaining implementation of the Nash solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 581-586.
  13. Naeve, Jorg, 1999. "Nash implementation of the Nash bargaining solution using intuitive message spaces," Economics Letters, Elsevier, vol. 62(1), pages 23-28, January.
  14. Elisabeth Naeve-Steinweg, 1999. "A note on van Damme's mechanism," Review of Economic Design, Springer;Society for Economic Design, vol. 4(2), pages 179-187.
  15. Gerber, Anke & Upmann, Thorsten, 2006. "Bargaining solutions at work: Qualitative differences in policy implications," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 162-175, September.
  16. Bergin, James & Duggan, John, 1999. "An Implementation-Theoretic Approach to Non-cooperative Foundations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 50-76, May.
  17. Trockel, Walter, 1996. "A Walrasian approach to bargaining games," Economics Letters, Elsevier, vol. 51(3), pages 295-301, June.
  18. Walter Trockel, 1999. "Integrating the Nash Program into Mechanism Theory," UCLA Economics Working Papers 787, UCLA Department of Economics.
  19. Damme, Eric van, 1986. "The Nash bargaining solution is optimal," Journal of Economic Theory, Elsevier, vol. 38(1), pages 78-100, February.
  20. Walter Trockel, 2000. "Implementations of the Nash solution based on its Walrasian characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(2), pages 277-294.
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