The equity core and the Lorenz-maximal allocations in the equal division core

Llerena, Francesc; Vilella, Cori

doi:10.1007/s00186-015-0494-0

Cited by 2 publications

(3 citation statements)

References 13 publications

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“…From (10) and (11) it follows that x |N \{i} satisfies the conditions stated in Theorem 1 (w.r.t. π ).…”

Section: Axiomatic Characterizationsmentioning

confidence: 88%

“…That is, σ 3 chooses the Lorenz maximal allocations in the imputation set. Llerena and Mauri (2015) show that this solution is single-valued and Lorenz dominates all core elements. Then, σ 3 satisfies individual rationality, internal Lorenz stability, external Lorenz stability (over the core), but not weak max consistency.…”

Section: Definition 4 the Egalitarian Core Of A Balanced Gamementioning

confidence: 89%

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On the existence of the Dutta–Ray’s egalitarian solution

Llerena

Mauri

2017

Mathematical Social Sciences

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A class of balanced games, called exact partition games, is introduced. Within this class, it is shown that the egalitarian solution of Dutta and Ray (1989) behaves as in the class of convex games. Moreover, we provide two axiomatic characterization by means of suitable properties such as consistency, rationality and Lorenz-fairness. As a by-product, alternative characterizations of the egalitarian solution over the class of convex games are obtained.

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“…From (10) and (11) it follows that x |N \{i} satisfies the conditions stated in Theorem 1 (w.r.t. π ).…”

Section: Axiomatic Characterizationsmentioning

confidence: 88%

Section: Definition 4 the Egalitarian Core Of A Balanced Gamementioning

confidence: 89%

On the existence of the Dutta–Ray’s egalitarian solution

Llerena

Mauri

2017

Mathematical Social Sciences

Self Cite

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“…Remark 5.5. For convex games in continuous variables, the Lorenz stable set is characterized by the Davis-Maschler reduced game property and the constrained egalitarianism (e.g., Arin-Inarra [1]) and, on the domain of essential games, the only single-valued solution satisfying the constrained egalitarianism and the projection consistency * is the Lorenz stable set [31]. Axiomatic characterizations of the Lorenz stable set in discrete convex games remains unsolved in our paper.…”

Section: Claimmentioning

confidence: 98%

Egalitarian Solution for Games With Discrete Side Payment

Otsuka

2021

JORSJ

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In this paper, we study the egalitarian solution for games with discrete side payment, where the characteristic function is integer-valued and payoffs of players are integral vectors. The egalitarian solution, introduced by Dutta and Ray in 1989, is a solution concept for transferable utility cooperative games in characteristic form, which combines commitment for egalitarianism and promotion of indivisual interests in a consistent manner. We first point out that the nice properties of the egalitarian solution (in the continuous case) do not extend to games with discrete side payment. Then we show that the Lorenz stable set, which may be regarded as a variant of the egalitarian solution, has nice properties such as the Davis-Maschler reduced game property and the converse reduced game property. For the proofs we utilize recent results in discrete convex analysis on decreasing minimization on an M-convex set investigated by Frank and Murota.

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The equity core and the Lorenz-maximal allocations in the equal division core

Cited by 2 publications

References 13 publications

On the existence of the Dutta–Ray’s egalitarian solution

On the existence of the Dutta–Ray’s egalitarian solution

Egalitarian Solution for Games With Discrete Side Payment

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