Considerations on the aggregate monotonicity of the nucleolus and the core-center

Given a claims problem, the average-of-awards rule ($${\text {AA}}$$ AA ) selects the expected value of the uniform distribution over the set of awards vectors. The $${\text {AA}}$$ AA rule is the center of gravity of the core of the coalitional game associated with a claims problem, so it corresponds to the core-center. We show that this rule satisfies a good number of properties so as to be included in the inventory of division rules. We also provide several representations of the $${\text {AA}}$$ AA rule and a procedure to compute it in terms of the parameters that define the problem.

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Axiomatizations of Dutta-Ray’s egalitarian solution on the domain of convex games

Calleja

Llerena

Sudhölter

2021

Journal of Mathematical Economics

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We show that on the domain of convex games, Dutta-Ray's egalitarian solution is characterized by core selection, aggregate monotonicity, and bounded richness, a new property requiring that the poorest players cannot be made richer within the core. Replacing "poorest" by "poorer" allows to eliminate aggregate monotonicity. Moreover, strengthening core selection into bilateral consistencyà la Davis and Maschler, and Pareto optimality into individual rationality and bilateral consistencyà la Hart and Mas-Colell, we obtain alternative and stylized axiomatic approaches.

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Considerations on the aggregate monotonicity of the nucleolus and the core-center

Cited by 3 publications

References 19 publications

Priority coalitional games and claims problems

Priority coalitional games and claims problems

The average-of-awards rule for claims problems

Axiomatizations of Dutta-Ray’s egalitarian solution on the domain of convex games

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