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**Two simple characterizations of the Nash bargaining solution.**
*(English)*
Zbl 1417.91245

Summary: We provide two alternative characterizations of the Nash bargaining solution. We introduce new simple axioms, strong undominatedness by the disagreement point, and egalitarian Pareto optimality. First, we prove that the Nash solution is characterized by symmetry, scale invariance, independence of irrelevant alternatives, and strong undominatedness by the disagreement point. Second, we replace the independence of irrelevant alternatives axiom with the sandwich axiom [S. Rachmilevitch, ibid. 80, No. 3, 427–442 (2016; Zbl 1378.91097)] and egalitarian Pareto optimality. We then demonstrate that the Nash solution is characterized by symmetry, scale invariance, strong undominatedness by the disagreement point, the sandwich axiom, and egalitarian Pareto optimality.

### MSC:

91B26 | Auctions, bargaining, bidding and selling, and other market models |

91A12 | Cooperative games |

91A05 | 2-person games |

### Keywords:

Nash bargaining solution; axiomatic characterization; strong undominatedness by disagreement point; sandwich axiom; egalitarian Pareto optimality### Citations:

Zbl 1378.91097
Full Text:
DOI

### References:

[1] | Anbarci, N, Simple characterizations of the Nash and Kalai smorodinsky solutions, Theory and Decision, 45, 255-261, (1998) · Zbl 0916.90280 |

[2] | Anbarci, N; Sun, C, Weakest collective rationality and the Nash bargaining solution, Social Choice and Welfare, 37, 425-429, (2011) · Zbl 1235.91070 |

[3] | Clippel, G, An axiomatization of the Nash bargaining solution, Social Choice and Welfare, 29, 201-210, (2007) · Zbl 1280.91018 |

[4] | Kalai, E; Smorodinsky, M, Other solutions to nash’s bargaining problem, Econometrica, 43, 513-518, (1975) · Zbl 0308.90053 |

[5] | Mariotti, M, Maximal symmetry and the Nash solution, Social Choice and Welfare, 17, 45-53, (2000) · Zbl 1069.91580 |

[6] | Nash, JF, The bargaining problem, Econometrica, 18, 155-162, (1950) · Zbl 1202.91122 |

[7] | Rachmilevitch, S, Egalitarian-Utilitarian bounds in nash’s bargaining problem, Theory and Decision, 80, 427-442, (2016) · Zbl 1378.91097 |

[8] | Roth, AE, Individual rationality and nash’s solution to the bargaining problem, Mathematics of Operations Research, 2, 64-65, (1977) · Zbl 0413.90089 |

[9] | Vartiainen, H, Collective choice with endogenous reference outcome, Games and Economic Behavior, 58, 172-180, (2007) · Zbl 1155.91317 |

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