No individual priorities and the Nash bargaining solution. (English) Zbl 1471.91191

Rachmilevitch, Shiran

Soc. Choice Welfare 56, No. 4, 855-863 (2021).

Summary: A bargaining solution satisfies no individual priorities (NIP) if the following holds: if \(x\) is the selected utility allocation and \(\pi x\) is also feasible, where \(\pi\) is some permutation, then \(x=\pi x\). I characterize the Nash bargaining solution on the basis of this axiom, non-triviality (the disagreement point is never selected), and scale covariance. An additional characterization is presented for the 2-person case, in which NIP is weakened and symmetry is added.

MSC:

91B26

Auctions, bargaining, bidding and selling, and other market models

References:

[1]	Anbarcı, N.; Sun, CJ, Weakest collective rationality and the Nash bargaining solution, Soc Choice Welf, 37, 425-429 (2011) · Zbl 1235.91070
[2]	Dagan, N.; Volij, O.; Winter, E., A characterization of the Nash bargaining solution, Soc Choice Welf, 19, 811-823 (2002) · Zbl 1072.91505
[3]	Kalai, E., Proportional solutions to bargaining situations: interpersonal utility comparisons, Econometrica, 45, 1623-1630 (1977) · Zbl 0371.90135
[4]	Kalai, E.; Smorodinsky, M., Other solutions to Nash’s bargaining problem, Econometrica, 43, 513-518 (1975) · Zbl 0308.90053
[5]	Lensberg, T.; Thomson, W., Characterizing the Nash bargaining solution without Pareto-optimality, Soc Choice Welf, 5, 247-259 (1988) · Zbl 0666.90096
[6]	Mariotti, M., Fair bargains: distributive justice and Nash bargaining theory, Rev Econ Stud, 66, 733-741 (1999) · Zbl 0942.91039
[7]	Mariotti, M., Maximal symmetry and the Nash solution, Soc Choice Welf, 17, 45-53 (2000) · Zbl 1069.91580
[8]	Mariotti, M., An ethical interpretation of the Nash choice rule, Theory Decis, 49, 151-157 (2000) · Zbl 0989.91029
[9]	Mori, O., Two simple characterizations of the Nash bargaining solution, Theory Decis, 85, 225-232 (2018) · Zbl 1417.91245
[10]	Nash, JF, The bargaining problem, Econometrica, 18, 155-162 (1950) · Zbl 1202.91122
[11]	Rachmilevitch, S., Nash bargaining with (almost) no rationality, Math Soc Sci, 76, 107-109 (2015) · Zbl 1331.91025
[12]	Roth, AE, Individual rationality and Nash’s solution to the bargaining problem, Math Oper Res, 2, 64-65 (1977) · Zbl 0413.90089
[13]	Roth, AE, Axiomatic models of bargaining. Lecture notes in economics and mathematical systems (1979), Berlin: Springer, Berlin
[14]	Sen, A., Collective choice and social welfare (1970), San Francisco: Holden-Day, San Francisco · Zbl 0227.90011
[15]	Suppes, P., Some formal models of grading principles, Synthese, 6, 284-306 (1966) · Zbl 0154.25803
[16]	Thomson, W., Cooperative models of bargaining, Handb Game Theory Econ Appl, 2, 1237-1284 (1994) · Zbl 0925.90084
[17]	Xu, Y., Symmetry-based compromise and the Nash solution to convex bargaining problems, Econ Lett, 115, 484-486 (2012) · Zbl 1253.91085