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An extension of the Nash bargaining problem and the Nash social welfare function


This paper provides an extension of Nash's bargaining model. The extension permits the domain of a solution function to contain non-convex sets. First, it is shown that the proposed extension is a mathematical generalization of Nash's bargaining problem. Next, some relations between the extension and the Nash social welfare function are developed. The formal equivalence of the two constructs is demonstrated, and the intuitive significance of the results is discussed.

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I am indebted to S. Ishikawa for helpful comments on an earlier draft and to K. Nakamura for helpful discussions. Any errors that remain are of course my responsibility.

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Kaneko, M. An extension of the Nash bargaining problem and the Nash social welfare function. Theor Decis 12, 135–148 (1980).

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  • Social Welfare
  • Solution Function
  • Social Welfare Function
  • Mathematical Generalization
  • Bargaining Model