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Bargaining with Non-convexities

  • Herings P. Jean-Jacques
  • Predtetchinski Arkadi


We show that in the canonical non-cooperative multilateral bargaining game, a subgameperfect equilibrium exists in pure stationary strategies, even when the space of feasible payoffs is not convex. At such an equilibrium there is no delay. We also have the converse result that randomization will not be used in this environment in the sense that all stationary subgame perfect equilibria do not involve randomization on the equilibrium path. Nevertheless, mixed strategy profiles can lead to Pareto superior payoffs in non-convex cases.

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Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 042.

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Date of creation: 2009
Date of revision:
Handle: RePEc:unm:umamet:2009042
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  1. Shimer, Robert, 2006. "On-the-job search and strategic bargaining," European Economic Review, Elsevier, vol. 50(4), pages 811-830, May.
  2. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-99, March.
  3. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  4. Herbert Scarf, 1994. "The Allocation of Resources in the Presence of Indivisibilities," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 111-128, Fall.
  5. Conley, John P. & Wilkie, Simon, 1996. "An Extension of the Nash Bargaining Solution to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 13(1), pages 26-38, March.
  6. 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.
  7. Kalandrakis, Tasos, 2004. "Equilibria in sequential bargaining games as solutions to systems of equations," Economics Letters, Elsevier, vol. 84(3), pages 407-411, September.
  8. In, Younghwan & Serrano, Roberto, 2004. "Agenda restrictions in multi-issue bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 53(3), pages 385-399, March.
  9. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  10. Tasos Kalandrakis, 2006. "Regularity of pure strategy equilibrium points in a class of bargaining games," Economic Theory, Springer, vol. 28(2), pages 309-329, 06.
  11. Xu, Yongsheng & Yoshihara, Naoki, 2006. "Alternative characterizations of three bargaining solutions for nonconvex problems," Games and Economic Behavior, Elsevier, vol. 57(1), pages 86-92, October.
  12. Herrero, Maria Jose, 1989. "The nash program: Non-convex bargaining problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 266-277, December.
  13. Eraslan, Hulya & Merlo, Antonio, 2002. "Majority Rule in a Stochastic Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 103(1), pages 31-48, March.
  14. Lang, Kevin & Rosenthal, Robert W, 2001. "Bargaining Piecemeal or All at Once?," Economic Journal, Royal Economic Society, vol. 111(473), pages 526-40, July.
  15. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
  16. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, June.
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