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Anchoring on Utopia: a generalization of the Kalai–Smorodinsky solution

Author

Listed:
  • Carlos Alós-Ferrer

    (University of Cologne)

  • Jaume García-Segarra

    (University of Cologne)

  • Miguel Ginés-Vilar

    (Universitat Jaume I de Castelló)

Abstract

Many bargaining solutions anchor on disagreement, allocating gains with respect to the worst-case scenario. We propose here a solution anchoring on utopia (the ideal, maximal aspirations for all agents), but yielding feasible allocations for any number of agents. The negotiated aspirations solution proposes the best allocation in the direction of utopia starting at an endogenous reference point which depends on both the utopia point and bargaining power. The Kalai–Smorodinsky solution becomes a particular case if (and only if) the reference point lies on the line from utopia to disagreement. We provide a characterization for the two-agent case relying only on standard axioms or natural restrictions thereof: strong Pareto optimality, scale invariance, restricted monotonicity, and restricted concavity. A characterization for the general (n-agent) case is obtained by relaxing Pareto optimality and adding the (standard) axiom of restricted contraction independence, plus the minimal condition that utopia should be selected if available.

Suggested Citation

  • Carlos Alós-Ferrer & Jaume García-Segarra & Miguel Ginés-Vilar, 2018. "Anchoring on Utopia: a generalization of the Kalai–Smorodinsky solution," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 141-155, October.
    • Handle: RePEc:spr:etbull:v:6:y:2018:i:2:d:10.1007_s40505-017-0130-7
    DOI: 10.1007/s40505-017-0130-7
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    More about this item

    Keywords

    n-Person bargaining; Utopia point; Axiomatic approach; Kalai–Smorodinsky solution;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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