Abstract
Any book on axiomatic bargaining game theory should start with Nash’s 1950 article and with the Nash bargaining solution, and so will this one. Without any doubt the Nash bargaining solution is the most well-known and popular solution concept in bargaining — in the theoretical literature as well as in applied and empirical work. What could be the reasons for this popularity? Empirical evidence for the Nash bargaining solution certainly is not overwhelming and besides, lack of empirical results concerning other solution concepts makes any comparison difficult if not impossible. (For some empirical work see Svejnar (1986), or van Cayseele (1987).) Further, many experiments have been conducted — see Roth and Malouf (1979) for an overview — but also these are not unambiguously conclusive in favor of the Nash solution. Even, earlier experiments by Crott (1971) point in the direction of the next popular solution, the Raiffa-Kalai-Smorodinsky solution (Raiffa, 1953, Kalai and Smorodinsky, 1975; see chapter 4).
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without loss of generality
This is obtained by first maximizing the first coordinate, conditionally on this maximizing the second coordinate, conditionally on this maximizing the third coordinate.
Bargaining games in (Math) may still be derived from expected utility bargaining situations if we relax condition (iii) in definition 1.2 in the appropriate way.
This shows that MCONV does not imply CONV. The construction of an example reflecting the converse implication is left to the reader.
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© 1992 Springer Science+Business Media Dordrecht
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Peters, H.J.M. (1992). Nash bargaining solutions. In: Axiomatic Bargaining Game Theory. Theory and Decision Library, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8022-9_2
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DOI: https://doi.org/10.1007/978-94-015-8022-9_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4178-4
Online ISBN: 978-94-015-8022-9
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