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Timing effect in bargaining and ex ante efficiency of the relative utilitarian solution. (English) Zbl 1397.91241
Summary: In this note, I provide an axiomatic characterization of the relative utilitarian bargaining solution (RU) to J. F. Nash jun. [Econometrica 18, 155–162 (1950; Zbl 1202.91122)] bargaining problems. The solution is obtained when Nash’s independence of irrelevant alternatives axiom is replaced by the weak linearity axiom, while retaining the other three axioms. RU maximizes the sum of proportional gains, or, equivalently, minimizes the sum of proportional losses. RU is scale invariant and compared to the solutions of Nash jun. [loc. cit.] and E. Kalai and M. Smorodinsky [Econometrica 43, 513–518 (1975; Zbl 0308.90053)], it is ex ante efficient when the bargaining problem is considered as a lottery of future bargaining problems.
##### MSC:
 91B26 Auctions, bargaining, bidding and selling, and other market models 91A12 Cooperative games
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