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Bargaining in networks and the myerson value

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  • Perea, Andrés
  • Navarro, Noemí

Abstract

We focus on a multiperson bargaining situation where the negotiation possibilities for the players are represented by a graph, that is, two players can negotiate directly with each other if and only if they are linked directly in the graph. The value of cooperation among players is given by a TU game. For the case where the graph is a tree and the TU game is strictly convex we present a noncooperative bargaining procedure, consisting of a sequence of bilateral negotiations, for which the unique subgame perfect equilibrium outcome coincides with the Myerson value of the induced graph-restricted game. In each bilateral negotiation, the corresponding pair of players bargains about the difference in payoffs to be received at the end. At the beginning of such negotiation there is a bidding stage in which both players announce prices. The player with the highest price becomes the proposer and makes a take-it-or-leave-it offer in terms of difference in payoffs to the other player. If the proposal is rejected, the proposer pays his announced price to the other player, after which this particular link is eliminated from the graph and the mechanism starts all over again for the remaining graph.

Suggested Citation

  • Perea, Andrés & Navarro, Noemí, 2001. "Bargaining in networks and the myerson value," UC3M Working papers. Economics we016121, Universidad Carlos III de Madrid. Departamento de Economía.
  • Handle: RePEc:cte:werepe:we016121
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    References listed on IDEAS

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    1. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    2. Suresh Mutuswami & David Pérez-Castrillo & David Wettstein, 2001. "Bidding for the Surplus: Realizing Efficient Outcomes in General Economic Environments," UFAE and IAE Working Papers 479.01, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    3. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
    4. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    5. Moulin, H., 1984. "Implementing the Kalai-Smorodinsky bargaining solution," Journal of Economic Theory, Elsevier, vol. 33(1), pages 32-45, June.
    6. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 255-273, March.
    7. (*), Y. Stephen Chiu & Ani Dasgupta, 1998. "On implementation via demand commitment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 161-189.
    8. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    9. Roger B. Myerson, 1976. "Graphs and Cooperation in Games," Discussion Papers 246, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Citations

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    Cited by:

    1. Noemí Navarro & Róbert Veszteg, 2008. "Threats and demonstrations of power: experimental results on bilateral bargaining," Working Papers 2008-11, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
    2. Noemí NAVARRO & Róbert VESZTEG, 2007. "Fair ultimatum: an experimental study of the Myerson value," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 07.05, Université de Lausanne, Faculté des HEC, DEEP.
    3. Matthew O. Jackson, 2003. "A survey of models of network formation: Stability and efficiency," Working Papers 1161, California Institute of Technology, Division of the Humanities and Social Sciences.
    4. Pin, Paolo, 2011. "Eight degrees of separation," Research in Economics, Elsevier, vol. 65(3), pages 259-270, September.
    5. Perez-Castrillo, David & Wettstein, David, 2005. "Forming efficient networks," Economics Letters, Elsevier, vol. 87(1), pages 83-87, April.
    6. Juan Vidal-Puga, 2003. "A bargaining approach to the consistent value for NTU games with coalition structure," Game Theory and Information 0303001, EconWPA.
    7. Navarro, Noemí & Veszteg, Róbert F., 2011. "Demonstration of power: Experimental results on bilateral bargaining," Journal of Economic Psychology, Elsevier, vol. 32(5), pages 762-772.
    8. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    9. Juan Vidal-Puga, 2005. "Implementation of the Levels Structure Value," Annals of Operations Research, Springer, vol. 137(1), pages 191-209, July.

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