27,108 research outputs found

    A note on equivalence of consistency and bilateral consistency through converse consistency

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    In the framework of (set-valued or single-valued) solutions for coalitional games with transferable utility, the three notions of consistency, bilateral consistency, and converse consistency are frequently used to provide axiomatic characterizations of a particular solution (like the core, prekernel, prenucleolus, Shapley value). Our main equivalence theorem claims that a solution satisfies consistency (with respect to an arbitrary reduced game) if and only if the solution satisfies both bilateral consistency and converse consistency (with respect to the same reduced game). The equivalence theorem presumes transitivity of the reduced game technique as well as difference independence on payoff vectors for two-person reduced games.\u

    Two axiomatizations of the kernel of TU games: bilateral and converse reduced game properties

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    We provide two axiomatic characterizations of the kernel of TU games by means of both bilateral consistency and converse consistency with respect to two types of two-person reduced games. According to the first type, the worth of any single player in the two-person reduced game is derived from the difference of player's positive (instead of maximum) surpluses. According to the second type, the worth of any single player in the two-person reduced game either coincides with the two-person max reduced game or refers to the constrained equal loss rule applied to an appropriate two-person bankruptcy problem, the claims of which are given by the player's positve surpluses

    A comparison of the average prekernel and the prekernel

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    We propose positive and normative foundations for the average prekernel of NTU games, and compare them with the existing ones for the prekernel. In our non-cooperative analysis, the average prekernel is approximated by the set of equilibrium payoffs of a game where each player faces the possibility of bargaining at random against any other player. In the cooperative analysis, we characterize the average prekernel as the unique solution that satisfies a set of Nash-like axioms for two-person games, and versions of average consistency and its converse for multilateral setting

    Consistency, converse consistency, and aspirations in TU-games

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    In problems of choosing ‘aspirations’ for TU-games, we study two axioms, ‘MW-consistency’ and ‘converse MW-consistency.’ In particular, we study which subsolutions of the aspiration correspondence satisfy MW-consistency and/or converse MW-consistency. We also provide axiomatic characterizations of the aspiration kernel and the aspiration nucleolus

    A COMPARISON OF THE AVERAGE PREKERNEL AND THE PREKERNEL

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    We propose positive and normative foundations for the average prekernel of NTU games, and compare them with the existing ones for the prekernel. In our non-cooperative analysis, the average prekernel is approximated by the set of equilibrium payoffs of a game where each player faces the possibility of bargaining at random against any other player. In the cooperative analysis, we characterize the average prekernel as the unique solution that satisfies a set of Nash-like axioms for two-person games, and versions of average consistency and its converse for multilateral settings

    A comparison of the average prekernel and the prekernel.

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    We propose positive and normative foundations for the average prekernel of NTU games, and compare them with the existing ones for the prekernel. In our non-cooperative analysis, the average prekernel is approximated by the set of equilibrium payoffs of a game where each player faces the possibility of bargaining at random against any other player. In the cooperative analysis, we characterize the average prekernel as the unique solution that satisfies a set of Nash-like axioms for two-person games, and versions of average consistency and its converse for multilateral settings

    Cooperative Multicriteria Games with Public and Private Criteria: An Investigation of Core Concepts

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    A new class of cooperative multicriteria games is introduced which takes into account two different types of criteria: private criteria, which correspond to divisible and excludable goods, and public criteria, which in an allocation take the same value for each coalition member. The different criteria are not condensed by means of a utility function, but left in their own right. Moreover, the games considered are not single-valued, but each coalition can realize a set of vectors - representing the outcomes of each of the criteria - depending on several alternatives. Two core concepts are defined: the core and the dominance outcome core. The relation between the two concepts is studied and the core is axiomatized by means of consistency properties.

    Consistency and the core for fuzzy non-transferable-utility games

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    Different from the works of Hwang (2007), we provide two extensions of the reduced games introduced by Moulin (1985) and Voorneveld and van den Nouweland (1998) on fuzzy non-transferable-utility (NTU) games, respectively. Based on the reduced games, we provide an axiomatization of the core and show that the technique of the proof in Tadenuma (1992) can not be applied to the core in the context of fuzzy NTU games.
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