Abstract
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.
Original language | English |
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Article number | 1235 |
Pages (from-to) | 1-19 |
Number of pages | 19 |
Journal | Mathematics |
Volume | 10 |
Issue number | 8 |
Early online date | 9 Apr 2022 |
DOIs | |
Publication status | Published - Apr 2022 |
Bibliographical note
Funding Information:This research has been partially supported by the ?Plan Nacional de I+D+i? of the Spanish Government under the project PID2020-116884GB-I00.
Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.
Funding
This research has been partially supported by the ?Plan Nacional de I+D+i? of the Spanish Government under the project PID2020-116884GB-I00.
Funders | Funder number |
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Secretaría de Estado de Investigacion, Desarrollo e Innovacion | PID2020-116884GB-I00 |
Keywords
- axiomatizations
- cooperative TU game
- directed communication
- directed graph
- position value