A position value for multigraphs

Abstract

Multicommunication is one of the methods at our disposal to address the significant challenges of reliability and latency in today’s communications. This paper presents a game-theoretical analysis of multicommunication, where we assume that players in a TU-game are restricted in their communication by a multigraph, whose links may or may not have limitations on capacity, frequency, or transmission speed. We generalize the classical position value defined for graph games to assess the importance of different communication providers. Extending to this context the classical properties of component efficiency and balanced link contributions we can characterize the new value. For a wide variety of multicommunications including but not limited to all those where the connections are in series or parallel, the value can be characterized by substituting balanced link contributions for the more restrictive balanced link pack contributions. In the case of limitations in capacity, parallel characterizations are obtained in which component efficiency must be substituted by a certain inefficiency that takes these limitations into account.