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Bargaining and Buyout

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  • Joosung Lee

Abstract

I introduce a noncooperative coalitional bargaining model for characteristic function form games. A player not only buys out other players' resources and rights with upfront transfers as in Gul (Econometrica, 1989), but also strategically chooses partners instead of bargaining with a randomly selected opponent. Such transactions among players are interpreted as coalition formation. The main theorem provides a general inefficiency result. If a characteristic function form game has a strict subcoalition with a strictly positive worth and a player with a strictly positive marginal contribution to the grand-coalition, then an efficient stationary subgame perfect equilibrium does not exist, as long as the discount factor is sufficiently high but strictly less than 1. Two special results are established. A grand-coalition equilibrium is impossible when players are sufficiently patient, unless the characteristic function form game is a unanimity game. For a simple game with a veto player and multiple winning coalitions, a non-minimal winning coalition is formed with positive probability. In two applications, I study players' strategic alliance behavior and the effect of the strategic behavior on inequality. First, for three-player simple games, the equilibrium payoff vector Lorenz-dominates both the Shapley-Shubik power index and the core-constrained Nash bargaining solution. Second, for wage bargaining games, workers endogenously form a union and their equilibrium payoffs can be greater than marginal products.

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Paper provided by Job Market Papers in its series 2013 Papers with number ple701.

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Date of creation: 20 Nov 2013
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Handle: RePEc:jmp:jm2013:ple701

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  1. Seidmann, Daniel J & Winter, Eyal, 1998. "A Theory of Gradual Coalition Formation," Review of Economic Studies, Wiley Blackwell, vol. 65(4), pages 793-815, October.
  2. Olivier Compte & Philippe Jehiel, 2010. "The Coalitional Nash Bargaining Solution," Econometrica, Econometric Society, vol. 78(5), pages 1593-1623, 09.
  3. Sergiu Hart & Andreu Mas-Colell, 1994. "Bargaining and value," Economics Working Papers 114, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 1995.
  4. Krishna, V. & Serrano, R., 1993. "Perfect Equilibria of a Model of N-Person Noncooperative Bargaining," Harvard Institute of Economic Research Working Papers 10, Harvard - Institute of Economic Research.
  5. Andrew McLennan & Hülya Eraslan, 2010. "Uniqueness of Stationary Equilibrium Payoffs in Coalitional Bargaining," Economics Working Paper Archive 562, The Johns Hopkins University,Department of Economics.
  6. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  7. Chatterjee, Kalyan & Bhaskar Dutta & Debraj Ray & Kunal Sengupta, 1993. "A Noncooperative Theory of Coalitional Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 60(2), pages 463-77, April.
  8. Morelli, Massimo & Montero, Maria, 2003. "The demand bargaining set: general characterization and application to majority games," Games and Economic Behavior, Elsevier, vol. 42(1), pages 137-155, January.
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  10. Debraj Ray & Rajiv Vohra, 2013. "Coalition Formation," Working Papers 2013-1, Brown University, Department of Economics.
  11. Serrano, Roberto, 1993. "Non-cooperative Implementation of the Nucleolus: The 3-Player Case," International Journal of Game Theory, Springer, vol. 22(4), pages 345-57.
  12. Lee, Joosung & Driessen, Theo S.H., 2012. "Sequentially two-leveled egalitarianism for TU games: Characterization and application," European Journal of Operational Research, Elsevier, vol. 220(3), pages 736-743.
  13. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May.
  14. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
  15. Montero, Maria, 2002. "Non-cooperative bargaining in apex games and the kernel," Games and Economic Behavior, Elsevier, vol. 41(2), pages 309-321, November.
  16. Montero, Maria & Vidal-Puga, Juan J., 2011. "Demand bargaining and proportional payoffs in majority games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 395-408, March.
  17. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer, vol. 23(1), pages 43-48.
  18. Cai, Hongbin, 2000. "Delay in Multilateral Bargaining under Complete Information," Journal of Economic Theory, Elsevier, vol. 93(2), pages 260-276, August.
  19. Eraslan, Hulya, 2002. "Uniqueness of Stationary Equilibrium Payoffs in the Baron-Ferejohn Model," Journal of Economic Theory, Elsevier, vol. 103(1), pages 11-30, March.
  20. Kyle Hyndman & Debraj Ray, 2007. "Coalition Formation with Binding Agreements," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1125-1147.
  21. Huibin Yan, 2003. "Noncooperative selection of the core," International Journal of Game Theory, Springer, vol. 31(4), pages 527-540, 09.
  22. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
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