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


Alós-Ferrer, Carlos; García-Segarra, Jaume; Ginés-Vilar, Miguel (2018). Anchoring on Utopia: a generalization of the Kalai–Smorodinsky solution. Economic Theory Bulletin, 6(2):141-155.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Uncontrolled Keywords:n-Person bargaining, utopia point, axiomatic approach, Kalai–Smorodinsky solution
Language:English
Date:1 October 2018
Deposited On:05 Jun 2018 10:24
Last Modified:01 Mar 2019 11:59
Publisher:Springer
ISSN:2196-1085
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s40505-017-0130-7
Official URL:https://link.springer.com/article/10.1007/s40505-017-0130-7

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