552 research outputs found

    Average tree solutions and the distribution of Harsanyi dividends

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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 \sl 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.

    Values for rooted-tree and sink-tree digraphs games and sharing a river

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    We introduce values for rooted-tree and sink-tree digraph games axiomatically and provide their explicit formula representation. These values may be considered as natural extensions of the lower equivalent and upper equivalent solutions for line-graph games studied in Brink, Laan, and Vasil'ev (2007). We study the distribution of Harsanyi dividends. We show that the problem of sharing a river with a delta or with multiple sources among different agents located at different levels along the riverbed can be embedded into the framework of a rooted-tree or sink-tree digraph game correspondingly

    Weighted Component Fairness for Forest Games

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    We present the axiom of weighted component fairness for the class of forest games, a generalization of component fairness introduced by Herings, Talman and van der Laan (2008) in order to characterize the average tree solution. Given a system of weights, component eciency and weighted component fairness yield a unique allocation rule. We provide an analysis of the set of allocation rules generated by component eciency and weighted component fairness. This allows us to provide a new characterization of the random tree solutions.(Weighted) component fairness ; Core ; Graph games ; Alexia value ; Harsanyi solutions ; Random tree solutions.

    Average tree solutions for graph games

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    In this paper we consider cooperative graph games being TU-games in which players cooperate if they are connected in the communication graph. We focus our attention to the average tree solutions introduced by Herings, van der Laan and Talman [6] and Herings, van der Laan, Talman and Yang [7]. Each average tree solution is defined with re- spect to a set, say T , of admissible rooted spanning trees. Each average tree solution is characterized by efficiency, linearity and an axiom of T - hierarchy on the class of all graph games with a fixed communication graph. We also establish that the set of admissible rooted spanning trees introduced by Herings, van der Laan, Talman and Yang [7] is the largest set of rooted spanning trees such that the corresponding aver- age tree solution is a Harsanyi solution. One the other hand, we show that this set of rooted spanning trees cannot be constructed by a dis- tributed algorithm. Finally, we propose a larger set of spanning trees which coincides with the set of all rooted spanning trees in clique-free graphs and that can be computed by a distributed algorithm.

    The Component Fairness Solution for Cycle- Free Graph Games

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    In this paper we study cooperative games with limited cooperation possibilities, representedby an undirected cycle-free communication graph. Players in the game can cooperate if andonly if they are connected in the graph, i.e. they can communicate with one another. Weintroduce a new single-valued solution concept, the component fairness solution. Our solution is characterized by component efficiency and component fairness. The interpretationof component fairness is that deleting a link between two players yields for both resultingcomponents the same average change in payoff, where the average is taken over the players in the component. Component fairness replaces the axiom of fairness characterizing the Myerson value, where the players whose link is deleted face the same loss in payoff. Thecomponent fairness solution is always in the core of the restricted game in case the gameis superadditive and can be easily computed as the average of n specific marginal vectors,where n is the number of players. We also show that the component fairness solution canbe generated by a specific distribution of the Harsanyi-dividends.operations research and management science;

    The Component Fairness Solution for Cycle-Free Graph Games

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    AMS classification: 90B18; 91A12; 91A43;TU-games;communication structure;Myerson value;fairness;marginal vector
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