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Reject and renegotiate: The Shapley value in multilateral bargaining

  • Ju, Yuan
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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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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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  1. Sun,N. & Trockel,W. & Yang,Z., 2004. "Competitive outcomes and endogenous coalition formation in an n-person game," Center for Mathematical Economics Working Papers 358, Center for Mathematical Economics, Bielefeld University.
  2. Ju, Y. & Wettstein, D., 2006. "Implementing Cooperative Solution Concepts : A Generalized Bidding Approach," Discussion Paper 2006-42, Tilburg University, Center for Economic Research.
  3. Faruk Gul, 1999. "Efficiency and Immediate Agreement: A Reply to Hart and Levy," Econometrica, Econometric Society, vol. 67(4), pages 913-918, July.
  4. Sergiu Hart & Andreu Mas-Colell, 1994. "Bargaining and value," Economics Working Papers 114, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 1995.
  5. David Pérez-Castrillo & David Wettstein, . "Bidding For The Surplus: A Non-Cooperative Approach To The Shapley Value," UFAE and IAE Working Papers 461.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  7. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  8. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
  9. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  10. Krishna, V. & serrano, R., 1993. "Perfect Equilibria of a Model of N-Person Noncooperative Bargaining," Papers 10-93-31, Pennsylvania State - Department of Economics.
  11. Walter Trockel, 1999. "Integrating the Nash Program into Mechanism Theory," UCLA Economics Working Papers 787, UCLA Department of Economics.
  12. David P�rez-Castrillo & David Wettstein, 2002. "Choosing Wisely: A Multibidding Approach," American Economic Review, American Economic Association, vol. 92(5), pages 1577-1587, December.
  13. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
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