Partially ordered cooperative games: extended core and Shapley value

Puerto, Justo; Fernández, Francisco R.; Hinojosa, Yolanda

doi:10.1007/s10479-007-0242-9

Cited by 20 publications

(9 citation statements)

References 19 publications

(28 reference statements)

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“…Alparslan Gök [1] choose to compare intervals in the following way, using the weakly better operator. That was inspired by Hinojosa et al [24]. Definition 10.…”

Section: Interval Analysismentioning

confidence: 99%

On convexity and solution concepts in cooperative interval games

Bok¹

2018

Preprint

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Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together.In this paper we study convexity, core and the Shapley value of games with interval uncertainty. Our motivation to do so is twofold. First, we want to capture which properties are preserved when we generalize concepts from classical cooperative game theory to interval games. Second, since these generalizations can be done in different ways, mainly with regard to the resulting level of uncertainty, we try to compare them and show their relation to each other.

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“…Alparslan Gök [1] choose to compare intervals in the following way, using the weakly better operator. That was inspired by Hinojosa et al [24]. Definition 10.…”

Section: Interval Analysismentioning

confidence: 99%

On convexity and solution concepts in cooperative interval games

Bok¹

2018

Preprint

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“…Alparslan Gök [1] choose an approach using a weakly better operator. That was inspired by [19]. Their definition of imputation and core is as follows.…”

Section: Cooperative Interval Gamesmentioning

confidence: 99%

Selection-Based Approach to Cooperative Interval Games

Bok

Hladík

2015

Operations Research and Enterprise Systems

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Abstract. Cooperative interval games are a generalized model of cooperative games in which the worth of every coalition corresponds to a closed interval representing the possible outcomes of its cooperation. Selections are all possible outcomes of the interval game with no additional uncertainty. We introduce new selection-based classes of interval games and prove their characterization theorems and relations to existing classes based on the interval weakly better operator. We show new results regarding the core and imputations and examine a problem of equivalence between two different versions of the core, which is the main stability solution of cooperative games. Then we introduce the definition of strong imputation and strong core as a universal solution concept of interval games.

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“…The other types of stochastic games were also proposed by Chakrabarti [7], Alvarez-Mena and Hernández-Lerma [8], Dshalalow and Huang [9], Dekel et al [10] and Guo and Yang [11]. A general model of cooperative games whose characteristic function takes values in a partially ordered linear space has also been studied by Puerto et al [12].…”

Section: Introductionmentioning

confidence: 96%

Interval-Valued Cores and Interval-Valued Dominance Cores of Cooperative Games Endowed with Interval-Valued Payoffs

2018

Mathematics

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Cooperative games endowed with interval-valued payoffs are studied in this paper. Based on the interval-valued payoff and the different types of orderings, we can propose many types of so-called interval-valued cores and interval-valued dominance cores. The main issue of this paper is to establish the equalities of different types of interval-valued cores and interval-valued dominance cores under a mild assumption. Without considering the individual rationality, we also establish the equalities of different types of interval-valued pre-cores and interval-valued dominance pre-cores without any extra assumptions.

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Partially ordered cooperative games: extended core and Shapley value

Cited by 20 publications

References 19 publications

On convexity and solution concepts in cooperative interval games

On convexity and solution concepts in cooperative interval games

Selection-Based Approach to Cooperative Interval Games

Interval-Valued Cores and Interval-Valued Dominance Cores of Cooperative Games Endowed with Interval-Valued Payoffs

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