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Bargaining In Networks And The Myerson Value

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  • Noemí Navarro

    ()

  • Andrés Perea

    ()

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.

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we016121.

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Date of creation: Nov 2001
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Handle: RePEc:cte:werepe:we016121

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References

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  1. (*), Y. Stephen Chiu & Ani Dasgupta, 1998. "On implementation via demand commitment games," International Journal of Game Theory, Springer, vol. 27(2), pages 161-189.
  2. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer, vol. 4(2), pages 255-73, March.
  3. Moulin, H., 1984. "Implementing the Kalai-Smorodinsky bargaining solution," Journal of Economic Theory, Elsevier, vol. 33(1), pages 32-45, June.
  4. 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).
  5. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  6. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
  8. 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).
  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. Matthew O. Jackson, 2003. "Allocation Rules for Network Games," Game Theory and Information 0303010, EconWPA.
  2. Juan Vidal-Puga, 2003. "Implementation of the levels structure value," Game Theory and Information 0303006, EconWPA.
  3. Paolo Pin, 2006. "Eight degrees of separation," Working Papers 2006_26, Department of Economics, University of Venice "Ca' Foscari".
  4. Matthew O. Jackson, 2003. "A Survey of Models of Network Formation: Stability and Efficiency," Game Theory and Information 0303011, EconWPA.
  5. 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.
  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. 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.

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