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Journal of Economic Interaction and Coordination

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20-12-2017 | Regular Article

Stagnation proofness in n-agent bargaining problems

Authors: Jaume García-Segarra, Miguel Ginés-Vilar

Published in: Journal of Economic Interaction and Coordination | Issue 1/2019

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

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

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 \(i \in I\), \(x_i> y_i\).

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

Alós-Ferrer C, García-Segarra J, Ginés-Vilar M (2017) Anchoring on Utopia: a generalization of the Kalai–Smorodinsky solution. Economic Theory Bulletin forthcoming

Chun Y, Peters HJH (1989) Lexicographic monotone path solutions. Op Res Spektrum 11(1):43–47CrossRef

Driesen B (2016) Truncated leximin solutions. Math Soc Sci 83:79–87CrossRef

Dubra J (2001) An asymmetric Kalai–Smorodinsky solution. Econ Lett 73(2):131–136CrossRef

García-Segarra J, Ginés-Vilar M (2015) The impossibility of paretian monotonic solutions: a strengthening of Roth’s result. Op Res Lett 43(5):476–478CrossRef

Herrero C (1998) Endougenous reference point and the adjusted proportional solution for bargaining problems with claims. Soc Choice Welf 15(1):113–119CrossRef

Herrero C, Marco MC (1993) Rational equal-loss solutions for bargaining problems. Math Soc Sci 26(3):273–286CrossRef

Imai H (1983) Individual monotonicity and lexicographic maxmin solution. Econometrica 51(2):389–401CrossRef

Kalai E (1977) Proportional solutions to bargaining situations: interpersonal utility comparisons. Econometrica 45(7):1623–1630CrossRef

Kalai E, Smorodinsky M (1975) Other solutions to Nash’s bargaining problem. Econometrica 43(3):513–518CrossRef

Nash JF (1950) The bargaining problem. Econometrica 18(2):155–162CrossRef

Peters HJH, Tijs SH (1984) Individually monotonic bargaining solutions of \(n\)-person bargaining games. Method Op Res 51:377–384

Peters HJH, Tijs SH (1985) Characterization of all individually monotonic bargaining solutions. Int J Game Theory 14(4):219–228CrossRef

Rosenthal RW (1976) An arbitration model for normal-form games. Math Op Res 1(1):82–88CrossRef

Salonen H (1987) Partially monotonic bargaining solutions. Soc Choice Welf 4(1):1–8CrossRef

Thomson W (1994) Cooperative models of bargaining. In: Aumann RJ, Hart S (eds) Handbook of game theory with economic applications, vol 2. Elsevier, Amsterdam, pp 1237–1284CrossRef

Thomson W, Myerson RB (1980) Monotonicity and independence axioms. Int J Game Theory 9(1):37–49CrossRef

Title: Stagnation proofness in n-agent bargaining problems
Authors: Jaume García-Segarra
Miguel Ginés-Vilar
Publication date: 20-12-2017
Publisher: Springer Berlin Heidelberg
Published in: Journal of Economic Interaction and Coordination / Issue 1/2019
Print ISSN: 1860-711X
Electronic ISSN: 1860-7128
DOI: https://doi.org/10.1007/s11403-017-0212-5

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