Radzvilas, Mantas
(2016):
*Hypothetical Bargaining and the Equilibrium Selection Problem in Non-Cooperative Games.*

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## Abstract

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.

Item Type: | MPRA Paper |
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Original Title: | Hypothetical Bargaining and the Equilibrium Selection Problem in Non-Cooperative Games |

English Title: | Hypothetical Bargaining and the Equilibrium Selection Problem in Non-Cooperative Games |

Language: | English |

Keywords: | Nash equilibrium, bargaining, equilibrium selection problem, Nash bargaining solution, correlated equilibrium, virtual bargaining, best-response reasoning |

Subjects: | C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory |

Item ID: | 70248 |

Depositing User: | Mr Mantas Radzvilas |

Date Deposited: | 24 Mar 2016 13:32 |

Last Modified: | 01 Oct 2019 20:52 |

References: | Aumann, R. J. (1987). “Correlated Equilibrium as an Expression of Bayesian Rationality”, Econometrica, pp.1-18. Aumann, R. J. and Brandenburger, A. (1995). “Epistemic Conditions for Nash Equilibrium”, Econometrica, 63, pp. 1161-1180. Bacharach, M. (2006). Beyond Individual Choice: Teams and Frames in Game Theory, Princeton: Princeton University Press. Bardsley, N., Mehta, J., Starmer, C. and Sugden, R. (2010). “Explaining Focal Points: Cognitive Hierarchy Theory versus Team Reasoning”, The Economic Journal, 120, pp. 40–79. Bernheim, D. (1984). “Rationalizable Strategic Behaviour”, Econometrica, 52, pp. 1007-1028. Binmore, K. G. (1980). “Nash Bargaining Theory I”, International Center for Economics and Related Disciplines, London School of Economics, Discussion Paper 80-09. Binmore, K. G., Rubinstein, A., Wolinsky, A. (1986). “The Nash Bargaining Solution in Economic Modelling”, RAND Journal of Economics, pp. 176-188. Cheng, S. Reeves, D. Vorobeychik, Y. Wellman, P. (2004). “Notes on Equilibria in Symmetric Games”, Proceedings of the 6th International Workshop On Game Theoretic And Decision Theoretic Agents GTDT 2004, pp. 71-78. Colman, A. M. and Stirk, J.A. (1998). “Stackelberg Reasoning in Mixed Motive Games: An Experimental Investigation”, Journal of Economic Psychology, 19, 279-293. Conley, J. P., Wilkie, S. (2012). “The Ordinal Egalitarian Bargaining Solution for Finite Choice Sets”, Social Choice and Welfare, 38, pp. 23-42. Fehr, E. and Schmidt, K. M. (1999). “A Theory of Fairness, Competition, and Cooperation”, Quarterly Journal of Economics, 114, pp. 817-868. Foley, D. (1967). “Resource Allocation and the Public Sector”, Yale Economic Essays, 7, pp. 45–98. Herreiner, D. K. and Puppe, C. D. (2009). “Envy-Freeness in Experimental Fair Division Problems”, Theory and Decision, 67, pp. 65-100. Hofbauer, J., Sigmund, K. (1998). Evolutionary Games and Population Dynamics. Cambridge: Cambridge University Press. Kalai, E. and Smorodinsky, M. (1975). “Other Solutions to Nash’s Bargaining Problem”, Econometrica, 43, pp. 513–518. Kalai, E. (1977). “Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons”, Econometrica, 45, pp. 1623–1630. Lehrer, E. Solan, E., Viossat, Y. (2011). “Equilibrium Payoffs of Finite Games”, Journal of Mathematical Economics, 2011, 47, pp. 48–53. Luce, R. D. and Raiffa, H. (1957). Games and Decisions: Introduction and Critical Survey. New York: Dover Publications, Inc. Misyak, J. and Chater, N. (2014). “Virtual Bargaining: A Theory of Social Decision-Making”, Philosophical Transactions of the Royal Society B, 369, pp. 1–9. Myerson, R. B. (1977). “Two-Person Bargaining Problems and Comparable Utility”, Econometrica, 45, pp. 1631–1637. Nash, J. (1951). “Non-Cooperative Games”, Annals of Mathematics, 54, pp. 286–295. Nydegger, R. and Owen, G. (1974). “Two-Person Bargaining: An Experimental Test of the Nash Axioms”, International Journal of Game Theory, 3, pp. 239–249. Olcina, G. and Urbano, A. (1994). “Introspection and Equilibrium Selection in 2x2 Matrix Games”, International Journal of Game Theory, 23, pp. 183-206. Pearce, D. (1984). “Rationalizable Startegic Behaviour and the Problem of Perfection”, Econometrica, 52, 1029-1050. Roth, A. (1979). “Proportional Solutions to the Bargaining Problem”, Econometrica, 47, pp. 775-778. Rubinstein, A. (1982). “Perfect Equilibrium in a Bargaining Model”, Econometrica, 50, pp. 97-109. Weller, D. (1985). “Fair Division of a Measurable Space”, Journal of Mathematical Economics, 14, pp. 5-17. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/70248 |