Two-bound core games and the nucleolus

Gong, Doudou; Dietzenbacher, Bas; Peters, Hans

doi:10.1007/s10479-022-04949-0

Cited by 5 publications

(1 citation statement)

References 12 publications

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“…In this paper, we focus on two-bound core games (cf. Gong et al 2022), i.e., games where the core is nonempty and can be described by a lower bound and an upper bound on the pre-imputations. Two-bound core games generalize compromise stable games (cf.…”

Section: Introductionmentioning

confidence: 99%

Reduced two-bound core games

2022

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This paper studies Davis–Maschler reduced games of two-bound core games and shows that all these reduced games with respect to core elements are two-bound core games with the same pair of bounds. Based on associated reduced game properties, we axiomatically characterize the core, the nucleolus, and the egalitarian core for two-bound core games. Moreover, we show that the egalitarian core for two-bound core games is single-valued and we provide an explicit expression.

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Section: Introductionmentioning

confidence: 99%

Reduced two-bound core games

2022

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One-bound core games

Gong,

Dietzenbacher,

Peters

2024

Int J Game Theory

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This paper introduces the new class of one-bound core games, where the core can be described by either a lower bound or an upper bound on the payoffs of the players, named lower bound core games and upper bound core games, respectively. We study the relation of the class of one-bound core games with several other classes of games and characterize the new class by the structure of the core and in terms of Davis-Maschler reduced games. We also provide explicit expressions and axiomatic characterizations of the nucleolus for one-bound core games, and show that the nucleolus coincides with the Shapley value and the $$\tau$$ τ -value when these games are convex.

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An algorithm to compute the average-of-awards rule for claims problems with an application to the allocation of CO$$_2$$ emissions

et al. 2023

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The set of awards vectors for a claims problem coincides with the core of the associated coalitional game. We analyze the structure of this set by defining for each group of claimants a, so called, utopia game, whose core comprises the most advantageous imputations available for the group. We show that, given a claims problem, the imputation set of the associated coalitional game can be partitioned by the cores of the utopia games. A rule selects for each claims problem a unique allocation from the set of awards vectors. The average-of-awards rule associates to each claims problem the geometric center of the corresponding set of awards vectors. Based on the decomposition of the imputation set, we obtain an interpretation of the average-of-awards rule as a point of fairness between stable and utopia imputations and provide a backward recurrence algorithm to compute it. To illustrate our analysis, we present an application to the distribution of CO$$_2$$ 2 emissions.

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Two-bound core games and the nucleolus

Cited by 5 publications

References 12 publications

Reduced two-bound core games

Reduced two-bound core games

One-bound core games

An algorithm to compute the average-of-awards rule for claims problems with an application to the allocation of CO$$_2$$ emissions

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