Latencies in multicommunication. A view from game theory

This paper presents an approach to the concept of latency in transferable utility games with communication restricted by a multigraph. Compared to graph games, multicommunication introduces into the analysis different possibilities of connection between players, depending on the use they make of the multiple edges (links between the same pair of players). We discuss four types of connectedness methods: maxmin, minmax, max and min, that are different ways of mixing series and parallel connectivity. Furthermore, we have assumed that both, players and links, have latencies, which have been introduced through random variables modeling delay in the negotiation processes for players and in the information transmission for links. Taking all these elements into account we have defined an allocation rule, the latency value, for transferable utility games with communication restricted by a multigraph and with latencies in players and links. This value performs very well with the replacement of multigraphs by simple graphs by adapting the latencies in a convenient way. In addition, the link in a graph replacing the multiple edges between two nodes in the multigraph, has a latency value that is the sum of the latency values of the edges in the multigraph it replaces.