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Nash demand game and the Kalai-Smorodinsky solution

  • Anbarci, Nejat
  • Boyd III, John H.

We introduce two new variations on the Nash demand game. In one, as in all past variants of Nash demand games, the Nash bargaining solution is the equilibrium outcome. The other demand game allows for probabilistic continuation in cases of infeasible joint demands. Specifically, with probability (1-p) the game terminates and the players receive their disagreement payoffs; but with probability p the game continues to a second stage in which one of the two incompatible demands is randomly selected and implemented. Surprisingly, the Kalai-Smorodinsky solution is always the outcome of the most robust equilibrium of this game. Moreover, ranking other solution concepts is impossible.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 71 (2011)
Issue (Month): 1 (January)
Pages: 14-22

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Handle: RePEc:eee:gamebe:v:71:y:2011:i:1:p:14-22
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Yusuke Samejima, 2005. "A Note on Implementation of Bargaining Solutions," Theory and Decision, Springer, vol. 59(3), pages 175-191, November.
  2. Rubinstein, Ariel & Safra, Zvi & Thomson, William, 1992. "On the Interpretation of the Nash Bargaining Solution and Its Extension to Non-expected Utility Preferences," Econometrica, Econometric Society, vol. 60(5), pages 1171-86, September.
  3. Ken Binmore, 1998. "Game Theory and the Social Contract - Vol. 2: Just Playing," MIT Press Books, The MIT Press, edition 1, volume 2, number 0262024446, June.
  4. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  5. Nejat Anbarci, 1995. "Reference Functions and Balanced Concessions in Bargaining," Canadian Journal of Economics, Canadian Economics Association, vol. 28(3), pages 675-82, August.
  6. Anbarci, Nejat, 1993. "Noncooperative Foundations of the Area Monotonic Solutions," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 245-58, February.
  7. Anbarci, Nejat & Bigelow, John P., 1994. "The area monotonic solution to the cooperative bargaining problem," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 133-142, October.
  8. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  10. Bigelow, John Payne & Anbarci, Nejat, 1993. "Non-dictatorial, Pareto-monotonic, cooperative bargaining : An impossibility theorem," European Journal of Political Economy, Elsevier, vol. 9(4), pages 551-558, November.
  11. Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
  12. Miyagawa, Eiichi, 2002. "Subgame-perfect implementation of bargaining solutions," Games and Economic Behavior, Elsevier, vol. 41(2), pages 292-308, November.
  13. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  14. 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.
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