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Stagnation proofness in n-agent bargaining problems

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Abstract

Some bargaining solutions may remain unchanged under any extension of a bargaining set which does not affect the utopia point, despite the fact that there is room to improve the utility of at least one agent. We call this phenomenon the stagnation effect. A bargaining solution satisfies stagnation proofness if it does not suffer from the stagnation effect. We show that stagnation proofness is compatible with the restricted version of strong monotonicity (Thomson and Myerson in Int J Game Theory 9(1):37–49, 1980), weak Pareto optimality, and scale invariance. The four axioms together characterize the family of the bargaining solutions generated by strictly-increasing paths ending at the utopia point (SIPUP-solutions).

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Notes

  1. The axioms of strong and weak Pareto optimality are formally defined in Sect. 1.

  2. See Thomson (1994) for a review of the main bargaining solutions in this literature.

  3. The basic mathematical notation is as follows: Let \(\{Y_i\}_{i\in I}\) be a family of sets \(Y_i\) indexed by I. We denote by \(y_J\) the projection of y onto \(Y^J\). If \(x,y \in \mathbb {R}^{I}\), then \(x\ge y \) means that, for each \(i \in I\), \(x_i\ge y_i\), analogously, \(x> y\) means that for each \(i \in I\), \(x_i> y_i\).

  4. We refer to this class of problems as the canonical bargaining problems.

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Author information

Authors and Affiliations

  1. Department of Economics, University of Cologne, Albertus-Magnus Platz, 50923, Cologne, Germany

    Jaume García-Segarra

  2. Department of Economics, Universitat Jaume I de Castelló, Av. de Vicent Sos Baynat s/n, 12071, Castellón, Spain

    Miguel Ginés-Vilar

Authors
  1. Jaume García-Segarra
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  2. Miguel Ginés-Vilar
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Corresponding author

Correspondence to Jaume García-Segarra.

Additional information

We are grateful to Carlos Alós-Ferrer, Carmen Herrero, J. Vte. Guinot, M.Carmen Marco, Hervé Moulin, Hans Peters, Hannu Salonen, William Thomson, and two anonymous referees for their useful comments. Financial support from projects ECO2015-68469-R Ministerio de Educación and PREDOC/2007/28 Fundación Bancaja, E-2011-27 Pla de Promoció de la Investigació de la UJI, P1-1B/2015/48 are gratefully acknowledged.

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García-Segarra, J., Ginés-Vilar, M. Stagnation proofness in n-agent bargaining problems. J Econ Interact Coord 14, 215–224 (2019). https://doi.org/10.1007/s11403-017-0212-5

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  • DOI: https://doi.org/10.1007/s11403-017-0212-5

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