The Average Tree Solution for Cooperative Games with Communication Structure

Herings, P. Jean-Jacques; Laan, Gerard van der; Talman, Dolf; Yang, Zaifu

doi:10.2139/ssrn.1263305

Cited by 19 publications

(37 citation statements)

References 17 publications

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“…Other characterizations on the class of cycle-free graph games have been provided by van den Brink (2009), Mishra and Talman (2010), Béal et al (2010Béal et al ( , 2012b and Ju and Park (2012). Generalizations of the AT solution to the class of all graph games have been examined by Herings et al (2010) and Baron et al (2011). The average tree solution has also been implemented by van den Brink et al (2013), and applied to and characterized in the richer frameworks of multichoice communication games by Béal et al (2012a) and of games with a permission tree by van den Brink et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Characterization of the Average Tree solution and its kernel

Béal

Rémila²,

Solal³

2015

Journal of Mathematical Economics

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In this article, we study cooperative games with limited cooperation possibilities, represented by a tree on the set of agents. Agents in the game can cooperate if they are connected in the tree. We first derive direct-sum decompositions of the space of TU-games on a fixed tree, and two new basis for these spaces of TU-games. We then focus our attention on the Average (rooted)-Tree solution (see Herings, P., van der Laan, G., Talman, D., 2008. The Average Tree Solution for Cycle-free Games. Games and Economic Behavior 62, 77-92). We provide a basis for its kernel and a new axiomatic characterization by using the classical axiom for inessential games, and two new axioms of invariance, namely Invariance with respect to irrelevant coalitions and Weighted addition invariance on bi-partitions.

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Section: Introductionmentioning

confidence: 99%

Characterization of the Average Tree solution and its kernel

Béal

Rémila²,

Solal³

2015

Journal of Mathematical Economics

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“…The condition of super-additivity was relaxed to a weaker one by Talman and Yamamoto [11]. In Herings et al [4] the average tree solution was generalized on the whole class of graph games, however no characterization was given there.…”

Section: Introductionmentioning

confidence: 99%

Parameterized fairness axioms on cycle-free graph games

2011

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Abstract. In this paper we study cooperative transferable utility games with communication structure represented by an undirected graph, i.e., a group of players can cooperate only if they are connected on the graph. This type of games is called graph games and the best-known solution for them is the Myerson value, characterized by component efficiency and fairness. Recently on cycle-free graph games, the average tree solution has been proposed and it is characterized by component efficiency and component fairness. We propose -parameterized fairness that incorporates the preceding fairness axioms on cycle-free graph games and show the existence and the uniqueness of a solution satisfying component efficiency and our fairness for any nonnegative parameter . We then discuss a relationship between the existing and our proposed solutions by a numerical example.

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“…One such solution, called the average tree solution, has been recently introduced and characterized by Herings et al [9] and Herings et al [10]. As for the Shapley value (Shapley, [16]) for cooperative games with transferable utilities, this solution relies on specific marginal contribution vectors.…”

Section: Introductionmentioning

confidence: 99%

“…Then we prove the following results. Firstly, the AT solution with respect to T is a Harsanyi solution if and only if T is a subset of the set of trees introduced in [10]. Secondly, the latter set is constructed by the classical DFS algorithm and the associated AT solution coincides with the Shapley value when the communication graph is complete.…”

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Average tree solutions and the distribution of Harsanyi dividends

et al. 2010

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We consider communication situations games being the combination of a TU-game and a communication graph. We study the average tree (AT) solutions introduced by Herings et al. [9] and [10]. The AT solutions are defined with respect to a set, say T , of rooted spanning trees of the communication graph. We characterize these solutions by efficiency, linearity and an axiom of T -hierarchy. Then we prove the following results. Firstly, the AT solution with respect to T is a Harsanyi solution if and only if T is a subset of the set of trees introduced in [10]. Secondly, the latter set is constructed by the classical DFS algorithm and the associated AT solution coincides with the Shapley value when the communication graph is complete. Thirdly, the AT solution with respect to trees constructed by the other classical algorithm BFS yields the equal surplus division when the communication graph is complete.

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The Average Tree Solution for Cooperative Games with Communication Structure

Cited by 19 publications

References 17 publications

Characterization of the Average Tree solution and its kernel

Characterization of the Average Tree solution and its kernel

Parameterized fairness axioms on cycle-free graph games

Average tree solutions and the distribution of Harsanyi dividends

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