Anchoring on Utopia: a generalization of the Kalai–Smorodinsky solution
- 111 Downloads
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.
Keywordsn-Person bargaining Utopia point Axiomatic approach Kalai–Smorodinsky solution
JEL ClassificationC71 C78
We are grateful to J. Vte. Guinot, Carmen Herrero, M. Carmen Marco, Juan D. Moreno-Ternero, Hervé Moulin, Hans Peters, Hannu Salonen, William Thomson, two anonymous referees and an associate editor for their useful comments. Financial support from projects ECO2015-68469 Ministerio de Educación, PREDOC/2007/28 Fundación Bancaja, and P1.15-1B2015-48 and E-2011-27 (Pla de Promoció de la Investigació) of the Universitat Jaume I are gratefully acknowledged.
- García-Segarra J.: Efficiency, Monotonicity, and Uncertainty in Bargaining Problems: an Axiomatic Approach. PhD thesis, Departament of Economics. Universitat Jaume I de Castelló (2015)Google Scholar
- Karagözoglu E, Keskin K, Özcan-Tok E (2015) Between anchors and aspirations: a new family of bargaining solutions, Working Paper, Bilkent UniversityGoogle Scholar
- Peters, H.J.H., Tijs, S.H.: Individually monotonic bargaining solutions of \(n\)-person bargaining games. Methods Oper. Res. 51, 377–384 (1984)Google Scholar
- Thomson W.: Cooperative models of bargaining. In: Aumann, R.J., Hart, S. (eds.) Handbook of Game Theory with Economic Applications, vol. 2, chap 35, pp. 1237–1284. Elsevier, Amsterdam (1994)Google Scholar