Characterization of the lexicographic egalitarian solution in the two-person bargaining problem.

*(English)*Zbl 1395.91235Summary: In this study, we provide a new characterization of the lexicographic egalitarian solution in the two-person bargaining problem using the independence of common monotone transformations axiom introduced by L. T. Nielsen [Econometrica 51, 219–221 (1983; Zbl 0501.90094)]. We introduce two new axioms, strict Suppes-Sen proofness and restricted equity. Strict Suppes-Sen proofness, which is analogous to M. Mariotti’s [Rev. Econ. Stud. 66, No. 3, 733–741 (1999; Zbl 0942.91039)] Suppes-Sen proofness, represents impartiality in the use of the strong Pareto optimality. Restricted equity represents the ethical notion that the more equitable distribution of utility gains relative to the disagreement point should be preferred if the total gain is fixed. Then, we show that the lexicographic egalitarian solution is characterized by strict Suppes-Sen proofness, restricted equity, and independence of common monotone transformations.

##### MSC:

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

91A12 | Cooperative games |

91A05 | 2-person games |

##### Keywords:

bargaining theory; axiomatic characterization; lexicographic egalitarian bargaining solution; independence of common monotone transformations; impartiality; equity##### References:

[1] | Mariotti, M., Fair bargains: distributive justice and Nash bargaining theory, Rev. Econom. Stud., 66, 733-741, (1999) · Zbl 0942.91039 |

[2] | Nash, J. F., The bargaining problem, Econometrica, 18, 155-162, (1950) · Zbl 1202.91122 |

[3] | Nielsen, L. T., Ordinal interpersonal comparisons in bargaining, Econometrica, 51, 219-221, (1983) · Zbl 0501.90094 |

[4] | Roth, A. E., Axiomatic Models of Bargaining, No. 170, (1979), Springer-Verlag Berlin, New York · Zbl 0408.90087 |

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