Abstract
We investigate the implications of the principle of welfare-domination under preference-replacement or replacement in the context of bargaining. It requires that changes in the preferences of some agents, unaccompanied by changes in the resources, should affect all of the agents whose preferences have not changed in the same direction: all gain or all lose together. We begin with investigating the logical relations between replacement and two monotonicity axioms, weak monotonicity and population monotonicity. Then, we establish characterizations of the Kalai–Smorodinsky and egalitarian solutions on the basis of replacement. On the other hand, we obtain impossibility results if Pareto optimality and replacement are imposed together with either strong individual rationality or symmetry.
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Notes
For a survey of the literature on the axiomatic bargaining theory, see Thomson (forthcoming).
Introduced under the name of independence of irrelevant alternatives.
Vector inequalities: given x, y ∈ R N, x≦y, x≤y, x<y. Set inclusions: given two sets S and T, S⊂T, S⊆T.
It requires that the naming of agents should not affect the solution outcome.
We borrow this argument from the proof of Theorem 2.10 in Thomson (forthcoming)
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This work was supported by the Brain Korea 21 Project in 2003. I am grateful to William Thomson, Hyungjun Kim, a referee, and an associate editor for their valuable comments.
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Chun, Y. The replacement principle in bargaining. Soc Choice Welfare 25, 141–154 (2005). https://doi.org/10.1007/s00355-005-0043-5
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DOI: https://doi.org/10.1007/s00355-005-0043-5