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Weakest collective rationality and the Nash bargaining solution. (English) Zbl 1235.91070
Summary: We propose a new axiom, weakest collective rationality (WCR) which is weaker than both weak Pareto optimality (WPO) in J. F. Nash jun.’s [Econometrica 18, 155–162 (1950; Zbl 1202.91122)] original characterization and strong individual rationality (SIR) in A. E. Roth [Math. Oper. Res. 2, 64–65 (1977; Zbl 0413.90089)] characterization of the Nash bargaining solution. We then characterize the Nash solution by symmetry (SYM), scale invariance (SI), independence of irrelevant alternatives (IIA) and our weakest collective rationality (WCR) axiom.
Reviewer: Reviewer (Berlin)

MSC:
91B26 Auctions, bargaining, bidding and selling, and other market models
91A26 Rationality and learning in game theory
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References:
[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] Nash JF (1950) The bargaining problem. Econometrica 18: 155–162 · Zbl 1202.91122 · doi:10.2307/1907266
[3] Roth AE (1977) Individual rationality and Nash’s solution to the bargaining problem. Math Oper Res 2: 64–65 · Zbl 0413.90089 · doi:10.1287/moor.2.1.64
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