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Reject and renegotiate: The Shapley value in multilateral bargaining

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  • Ju, Yuan
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Abstract

This paper investigates three distinctive and intuitive renegotiation bargaining protocols that all yield the Shapley value as the unique subgame perfect equilibrium outcome. These protocols, built on the multi-bidding procedure of Pérez-Castrillo and Wettstein (2001), allow more freedom in multilateral bargaining where rejected players can further negotiate and form coalitions. The self-duality of the Shapley value plays a key role in the second and third results. Moreover, these renegotiation protocols allow an actual play along the equilibrium path to restore the Shapley value in case of a ‘mistake’ made before.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 48 (2012)
Issue (Month): 6 ()
Pages: 431-436

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Handle: RePEc:eee:mateco:v:48:y:2012:i:6:p:431-436

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Bargaining; Subgame perfect equilibrium; Shapley value; Renegotiation;

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  1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, Econometric Society, vol. 18(2), pages 155-162, April.
  2. David P�rez-Castrillo & David Wettstein, 2002. "Choosing Wisely: A Multibidding Approach," American Economic Review, American Economic Association, American Economic Association, vol. 92(5), pages 1577-1587, December.
  3. Sergiu Hart & Andreu Mas-Colell, 1994. "Bargaining and value," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 114, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 1995.
  4. Sun, N. & Trockel, W. & Yang, Z.F., 2004. "Competitive Outcomes and Endogenous Coalition Formation in an n-Person Game," Discussion Paper, Tilburg University, Center for Economic Research 2004-93, Tilburg University, Center for Economic Research.
  5. Walter Trockel, 2002. "Integrating the Nash program into mechanism theory," Review of Economic Design, Springer, Springer, vol. 7(1), pages 27-43.
  6. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, Springer, vol. 18(4), pages 655-708.
  7. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, Econometric Society, vol. 57(1), pages 81-95, January.
  8. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, Elsevier, vol. 100(2), pages 274-294, October.
  9. Krishna, Vijay & Serrano, Roberto, 1995. "Perfect Equilibria of a Model of N-Person Noncooperative Bargaining," International Journal of Game Theory, Springer, Springer, vol. 24(3), pages 259-72.
  10. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, Fundación SEPI, vol. 29(2), pages 219-258, May.
  11. Ju, Y. & Wettstein, D., 2006. "Implementing Cooperative Solution Concepts: A Generalized Bidding Approach," Discussion Paper, Tilburg University, Center for Economic Research 2006-42, Tilburg University, Center for Economic Research.
  12. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, Econometric Society, vol. 21(1), pages 128-140, April.
  13. Faruk Gul, 1999. "Efficiency and Immediate Agreement: A Reply to Hart and Levy," Econometrica, Econometric Society, Econometric Society, vol. 67(4), pages 913-918, July.
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