Axiomatizing core extensions

Bejan, Camelia; Gómez, Juan Camilo

doi:10.1007/s00182-011-0316-4

Cited by 13 publications

(17 citation statements)

References 22 publications

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“…Moreover, given any second best time allocation in the original TU-game, under certain conditions, we provide a formula to compute the corresponding second best time allocation in any of its reduced games. Our axioms of superadditivity and consistency do not coincide with those of Peleg (1986) and their generalized versions in Bejan and Gómez (2012) on the set of balanced TU-games. The article is organized as follows.…”

Section: Introductionmentioning

confidence: 75%

“…Traditional reduced games (Davis and Maschler, 1965) used by Peleg (1986) make an exception to the grand coalition in order to ensure grand coalition feasibility. Bejan and Gómez (2012) use a more general version (Moldovanu and Winter, 1994) that treats all coalitions in the same way. Our axiom of consistency is based on a new modified version of reduced games which makes again an exception to the grand coalition.…”

Section: Introductionmentioning

confidence: 99%

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Optimal deterrence of cooperation

Gonzalez

Lardon

2017

Int J Game Theory

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We introduce axiomatically a new solution concept for cooperative games with transferable utility inspired by the core. While core solution concepts have investigated the sustainability of cooperation among players, our solution concept, called contraction core, focuses on the deterrence of cooperation. The main interest of the contraction core is to provide a monetary measure of the robustness of cooperation in the grand coalition. We motivate this concept by providing optimal fine imposed by competition authorities for the dismantling of cartels in oligopolistic markets. We characterize the contraction core on the set of balanced cooperative games with transferable utility by four axioms: the two classic axioms of non-emptiness and individual rationality, a superadditivity principle and a weak version of a new axiom of consistency.

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Section: Introductionmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Optimal deterrence of cooperation

Gonzalez

Lardon

2017

Int J Game Theory

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“…b When I was writing the final revision of this paper, P. Arribillaga called my attention to Bejan and Gomez (2012), where the authors provide an axiomatic characterization of the Aspiration Core (Bennett, 1983). The Aspiration Core coincides with the set of utility distributions of the imputations in the M-core.…”

Section: Discussionmentioning

confidence: 99%

Nonempty Core-Type Solutions Over Balanced Coalitions in Tu-Games

Cesco

2012

Int. Game Theory Rev.

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In this paper we introduce two related core-type solutions for games with transferable utility (TU-games) the B-core and the M-core. The elements of the solutions are pairs (x, B), where x, as usual, is a vector representing a distribution of utility and B is a balanced family of coalitions, in the case of the B-core, and a minimal balanced one, in the case of the M-core, describing a plausible organization of the players to achieve the vector x. Both solutions extend the notion of classical core but, unlike it, they are always nonempty for any TU-game. For the M-core, which also exhibits a certain kind of "minimality" property, we provide a nice axiomatic characterization in terms of the four axioms nonemptiness (NE), individual rationality (IR), superadditivity (SUPA) and a weak reduced game property (WRGP) (with appropriate modifications to adapt them to the new framework) used to characterize the classical core. However, an additional axiom, the axiom of equal opportunity is required. It roughly states that if (x, B) belongs to the M-core then, any other admissible element of the form (x, B ) should belong to the solution too.

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“…The inclusions where shown by, e.g., Bejan and Gómez (2012b), and the last equality by Cross (1967) and Bennett (1983).…”

Section: And Equality Holds Everywhere If and Only If V Is Balancedmentioning

confidence: 99%

“…(Bejan and Gómez 2012b) the minimum amount to be given to the grand coalition in order to ensure balancedness.…”

Section: Theorem 2 (The Bondareva-shapley Theorem Sharp Form) a Necmentioning

confidence: 99%

Autonomous coalitions

Gonzalez

Grabisch

2015

Ann Oper Res

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We consider in this paper solutions for TU-games where it is not assumed that the grand coalition is necessarily the final state of cooperation. Partitions of the grand coalition, or balanced collections together with a system of balancing weights interpreted as a time allocation vector are considered as possible states of cooperation. The former case corresponds to the c-core, while the latter corresponds to the aspiration core or d-core, where in both case, the best configuration (called a maximising collection) is sought. We study maximising collections and characterize them with autonomous coalitions, that is, coalitions for which any solution of the d-core yields a payment for that coalition equal to its worth. In particular we show that the collection of autonomous coalitions is balanced, and that one cannot have at the same time a single possible payment (core element) and a single possible configuration. We also introduce the notion of inescapable coalitions, that is, those present in every maximising collection. We characterize the class of games for which the sets of autonomous coalitions, vital coalitions (in the sense of Shellshear and Sudhölter), and inescapable coalitions coincide, and prove that the set of games having a unique maximising coalition is dense in the set of games.

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Axiomatizing core extensions

Cited by 13 publications

References 22 publications

Optimal deterrence of cooperation

Optimal deterrence of cooperation

Nonempty Core-Type Solutions Over Balanced Coalitions in Tu-Games

Autonomous coalitions

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