On the set of extreme core allocations for minimal cost spanning tree problems

Trudeau, Christian; Vidal-Puga, Juan

doi:10.1016/j.jet.2017.03.001

Cited by 19 publications

(16 citation statements)

References 28 publications

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“…Proof. Correspondence between the cycle-complete solution andȳ is shown in Trudeau and Vidal-Puga (2017). We show the correspondence between the nucleolus and the cycle-complete solution.…”

Section: Minimum Cost Spanning Tree Games and Clique Gamesmentioning

confidence: 70%

Clique games: A family of games with coincidence between the nucleolus and the Shapley value

Trudeau

Vidal-Puga

2020

Mathematical Social Sciences

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We introduce a new family of cooperative games for which there is coincidence between the nucleolus and the Shapley value. These socalled clique games are such that players are divided into cliques, with the value created by a coalition linearly increasing with the number of agents belonging to the same clique. Agents can belong to multiple cliques, but for a pair of cliques, at most a single agent belong to their intersection. Finally, if two players do not belong to the same clique, there is at most one way to link the two players through a chain of players, with any two adjacent players in the chain belonging to a common clique. We provide multiple examples for clique games, chief among them minimum cost spanning tree problems. This allows us to obtain new correspondence results between the nucleolus and the Shapley value, as well as other cost sharing methods for the minimum cost spanning tree problem.

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Section: Minimum Cost Spanning Tree Games and Clique Gamesmentioning

confidence: 70%

Clique games: A family of games with coincidence between the nucleolus and the Shapley value

Trudeau

Vidal-Puga

2020

Mathematical Social Sciences

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“…In [18,19] it is shown that for elementary mcst problems, the Folk solution is the permutationweighted average of the extreme points of the non-property rights game defined by v(S). Then, for any elementary mcst problem (N ω , C), as a consequence of Proposition 2 we obtain…”

Section: Some Further Commentsmentioning

confidence: 99%

“…. ., K, denote the extreme points of the core of the cooperative game defined by v(S) (see [18]). Moreover, in this class of mcst problems, β ceq also coincides with the nucleolus (see [19]), showing the close relationships between the egalitarian and nucleolus concepts.…”

Section: Some Further Commentsmentioning

confidence: 99%

An egalitarian approach for sharing the cost of a spanning tree

2020

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A minimum cost spanning tree problem analyzes the way to efficiently connect individuals to a source. Hence the question is how to fairly allocate the total cost among these agents. Our approach, reinterpreting the spanning tree cost allocation as a claims problem defines a simple way to allocate the optimal cost with two main criteria: (1) each individual only pays attention to a few connection costs (the total cost of the optimal network and the cost of connecting himself to the source); and (2) an egalitarian criteria is used to share costs. Then, using claims rules, we define an egalitarian solution so that the total cost is allocated as equally as possible. We show that this solutions could propose allocations outside the core, a counter-intuitive fact whenever cooperation is necessary. Then we propose a modification to get a core selection, obtaining in this case an alternative interpretation of the Folk solution.

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“…冷漠参与人的存在可能会使得相应博弈的核为空. 文献 [22] 给出了最小支撑树博弈核多面体所有的顶点, 并指出了最小支撑树博弈可能与指派博弈 (assignment games) 之间存在一定的联系. 文献 [23] 研究了最小支撑树问题中的机制设计问题, 发现如果使用 Folk 配置分担成本, 那么存在一个 Nash 均衡, 参与人都会真实报告自己的成本信息, 而使用 Bird 配置或者 DK 配置则不存在这样的均衡.…”

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