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Hypothetical Bargaining and the Equilibrium Selection Problem in Non-Cooperative Games

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  • Radzvilas, Mantas
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    Orthodox game theory is often criticized for its inability to single out intuitively compelling Nash equilibria in non-cooperative games. The theory of virtual bargaining, developed by Misyak and Chater (2014) suggests that players resolve non-cooperative games by making their strategy choices on the basis of what they would agree to play if they could openly bargain. The proposed formal model of bargaining, however, has limited applicability in non-cooperative games due to its reliance on the existence of a unique non-agreement point – a condition that is not satisfied by games with multiple Nash equilibria. In this paper, I propose a model of ordinal hypothetical bargaining, called the Benefit-Equilibration Reasoning, which does not rely on the existence of a unique reference point, and offers a solution to the equilibrium selection problem in a broad class of non-cooperative games. I provide a formal characterization of the solution, and discuss the theoretical predictions of the suggested model in several experimentally relevant games.

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    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 70248.

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    Date of creation: 24 Mar 2016
    Handle: RePEc:pra:mprapa:70248
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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    3. Nicholas Bardsley & Judith Mehta & Chris Starmer & Robert Sugden, 2010. "Explaining Focal Points: Cognitive Hierarchy Theory "versus" Team Reasoning," Economic Journal, Royal Economic Society, vol. 120(543), pages 40-79, March.
    4. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    5. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    6. Michael Bacharach, 2006. "The Hi-Lo Paradox, from Beyond Individual Choice: Teams and Frames in Game Theory," Introductory Chapters,in: Natalie Gold & Robert Sugden (ed.), Beyond Individual Choice: Teams and Frames in Game Theory Princeton University Press.
    7. Roth, Alvin E, 1979. "Proportional Solutions to the Bargaining Problem," Econometrica, Econometric Society, vol. 47(3), pages 775-777, May.
    8. Myerson, Roger B, 1977. "Two-Person Bargaining Problems and Comparable Utility," Econometrica, Econometric Society, vol. 45(7), pages 1631-1637, October.
    9. Dorothea Herreiner & Clemens Puppe, 2009. "Envy Freeness in Experimental Fair Division Problems," Theory and Decision, Springer, vol. 67(1), pages 65-100, July.
    10. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    11. Colman, Andrew M. & Stirk, Jonathan A., 1998. "Stackelberg reasoning in mixed-motive games: An experimental investigation," Journal of Economic Psychology, Elsevier, vol. 19(2), pages 279-293, April.
    12. John Conley & Simon Wilkie, 2012. "The ordinal egalitarian bargaining solution for finite choice sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 23-42, January.
    13. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February.
    14. Gonzalo Olcina Vauteren & Amparo Urbano Salvador, 1993. "INTROSPECTION AND EQUILIBRIUM SELECTION IN 2x2 MATRIX GAMES," Working Papers. Serie AD 1993-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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