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Nondiscrimination and monotonicity in fair division. (English) Zbl 1233.91162
Summary: Conditions one might impose on fair allocation procedures are introduced. Nondiscrimination requires that agents share an item in proportion to their entitlements if they receive nothing else. The “price” procedures of the author [J. Risk Uncertain. 35, No. 3, 203–236 (2007; Zbl 1133.91390)], including the Nash bargaining procedure, satisfy this. Other prominent efficient procedures do not.
MSC:
91B32 Resource and cost allocation (including fair division, apportionment, etc.)
91B26 Auctions, bargaining, bidding and selling, and other market models
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[1] Kalai, E., & Smorodinsky, M. (1975). Other solutions to Nash’s bargaining problem. Econometrica, 43, 513–518. · Zbl 0308.90053 · doi:10.2307/1914280
[2] Machina, M. J., & Pratt, J. W. (1997). Increasing risk: some direct constructions. Journal of Risk and Uncertainty, 14, 103–127. · Zbl 0886.90052 · doi:10.1023/A:1007719626543
[3] Pratt, J. W. (2007). Fair (and not so fair) division. Journal of Risk and Uncertainty, 35, 203–236. · Zbl 1133.91390 · doi:10.1007/s11166-007-9025-6
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