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Bargaining with independence of higher or irrelevant claims. (English) Zbl 1457.91190

Summary: This paper studies independence of higher claims and independence of irrelevant claims on the domain of bargaining problems with claims. Independence of higher claims requires that the payoff of an agent does not depend on the higher claim of another agent. Independence of irrelevant claims states that the payoffs should not change when the claims decrease but remain higher than the payoffs. Interestingly, in conjunction with standard axioms from bargaining theory, these properties characterize a new constrained Nash solution, a constrained Kalai-Smorodinsky solution, and a constrained Kalai solution.

MSC:

91B26 Auctions, bargaining, bidding and selling, and other market models
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References:

[1] Bossert, W., An alternative solution to bargaining problems with claims, Math. Social Sci., 25, 3, 205-220 (1993) · Zbl 0776.90091
[2] Chun, Y.; Peters, H., The lexicographic egalitarian solution, Cahiers CERO, 30, 149-156 (1988) · Zbl 0665.90101
[3] Chun, Y.; Thomson, W., Bargaining problems with claims, Math. Social Sci., 24, 1, 19-33 (1992) · Zbl 0769.90082
[4] Dagan, N.; Volij, O., The bankruptcy problem: a cooperative bargaining approach, Math. Social Sci., 26, 3, 287-297 (1993) · Zbl 0805.90123
[5] Dietzenbacher, B.; Estévez-Fernández, A.; Borm, P.; Hendrickx, R., Proportionality, equality, and duality in bankruptcy problems with nontransferable utility, Ann. Oper. Res. (2020)
[6] Dietzenbacher, B.; Peters, H., Characterizing NTU-bankruptcy rules using bargaining axiomsCentER Discussion Paper 2018-005 (2018)
[7] Gupta, S.; Livne, Z., Resolving a conflict situation with a reference outcome: an axiomatic model, Manage. Sci., 34, 11, 1303-1314 (1988) · Zbl 0663.90103
[8] Herrero, C.; Villar, A., The rights egalitarian solution for NTU sharing problems, Internat. J. Game Theory, 39, 1, 137-150 (2010) · Zbl 1211.91036
[9] Kalai, E., Proportional solutions to bargaining situations: interpersonal utility comparisons, Econometrica, 45, 7, 1623-1630 (1977) · Zbl 0371.90135
[10] Kalai, E.; Smorodinsky, M., Other solutions to Nash’s bargaining problem, Econometrica, 43, 3, 513-518 (1975) · Zbl 0308.90053
[11] Kibris, Ö., A revealed preference analysis of solutions to simple allocation problems, Theory and Decision, 72, 4, 509-523 (2012) · Zbl 1241.91041
[12] Lombardi, M.; Yoshihara, N., Alternative characterizations of the proportional solution for nonconvex bargaining problems with claims, Econom. Lett., 108, 2, 229-232 (2010) · Zbl 1230.91062
[13] Marco-Gil, M., An alternative characterization of the extended claim-egalitarian solution, Econom. Lett., 45, 1, 41-46 (1994) · Zbl 0801.90130
[14] Mariotti, M.; Villar, A., The Nash rationing problem, Internat. J. Game Theory, 33, 3, 367-377 (2005) · Zbl 1086.91038
[15] Moulin, H.; Shenker, S., Serial cost sharing, Econometrica, 60, 5, 1009-1037 (1992) · Zbl 0766.90013
[16] Nash, J., The bargaining problem, Econometrica, 18, 2, 155-162 (1950) · Zbl 1202.91122
[17] O’Neill, B., A problem of rights arbitration from the Talmud, Math. Social Sci., 2, 4, 345-371 (1982) · Zbl 0489.90090
[18] Orshan, G.; Valenciano, F.; Zarzuelo, J., The bilateral consistent prekernel, the core, and NTU bankruptcy problems, Math. Oper. Res., 28, 2, 268-282 (2003) · Zbl 1082.91020
[19] Stovall, J., Collective rationality and monotone path division rules, J. Econom. Theory, 154, 1-24 (2014) · Zbl 1309.91081
[20] Sudhölter, P.; Zarzuelo, J., Extending the Nash solution to choice problems with reference points, Games Econom. Behav., 80, 219-228 (2013) · Zbl 1281.91016
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