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Bargaining over the division of a shrinking pie: An axiomatic approach

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Abstract

The Bargaining Problem paradigm is extended to time-consuming conflict situations. Such a situation can be represented by a chain of bargaining domains, each representing the conflict at a different point in time. The solution function selects a point in the union of all these domains. We characterize a solution function which satisfies several requirements and explore its properties. One of the results is that an extension of the Adding requirement (Thomson-Myerson 1980) is enough, under some conditions, to yield a solution point, so there is no need to extend the stronger requirements of Independence of Irrelevant Alternatives (Nash 1950) or Monotonicity (Kalai-Smorodinsky 1975).

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Authors and Affiliations

  1. Faculty of Management, Tel Aviv University, 66978, Tel Aviv, Israel

    Z. Livne

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  1. Z. Livne
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Additional information

This paper is based on part of my 1979 Ph.D. dissertation at MIT. Its preparation was partially sponsored by the Office of Naval Research Contract Number N00 014-77-C-0518. I am grateful to H. Raiffa, G. Kaufman, J. Ferreira, E. Kohlberg and the referees for valuable comments.

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Livne, Z. Bargaining over the division of a shrinking pie: An axiomatic approach. Int J Game Theory 16, 223–242 (1987). https://doi.org/10.1007/BF01756293

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  • DOI: https://doi.org/10.1007/BF01756293

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