2026-06-29T16:49:27Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/919442025-07-08T08:33:31Zcom_20.500.14352_14col_20.500.14352_15

00925njm 22002777a 4500 dc Manuel García, Conrado Miguel author Gavilán García, Elena del Carmen author van den Brink, René author 2022 In this paper, we define a family of values for directed communication situations that are inspired by the position value. We use the concept of directed communication and related connectedness in directed graphs, under which a coalition of players in a game can only cooperate if these players form a directed path in a directed communication graph. By defining an arc game, which assesses the worth of coalitions of (directed) arcs in generating worth, we allocate the Shapley value payoff of each arc over the nodes incident with this arc, where we allow the head and tail to obtain a different share in this arc payoff. However, the way that the arc payoff is shared over its head and tail is uniform over all arcs. We characterize these values by connection efficiency and a modification of the classical balanced link contributions property for undirected communication situations, discriminating between the roles of the nodes as head and tail. Gavilán, E.C., Manuel, C.M. y van den Brink, R. (2022) «A Family of Position Values for Directed Communication Situations», Mathematics, 10(8). doi:10.3390/MATH10081235. 10.3390/MATH10081235 https://hdl.handle.net/20.500.14352/91944 https//doi.org/10.3390/MATH10081235 https://www.mdpi.com/2227-7390/10/8/1235 A Family of Position Values for Directed Communication Situations