We study a type of cooperative games introduced in [8] called shortest path games. They arise on a network that has two special nodes s and t. A coalition corresponds to a set of arcs and it receives a reward if it can connect s and t. A coalition also incurs a cost for each arc that it uses to connect s and t, thus the coalition must choose a path of minimum cost among all the arcs that it controls. These games are relevant to logistics, communication, or supply-chain networks. We give a polynomial combinatorial algorithm to compute the nucleolus. This vector reflects the relative importance of each arc to ensure the connectivity between s and t. Our development is done on a directed graph, but it can be extended to undirected graphs and to similar games defined on the nodes of a graph.
CITATION STYLE
Baïou, M., & Barahona, F. (2017). On the nucleolus of shortest path games. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10504 LNCS, pp. 55–66). Springer Verlag. https://doi.org/10.1007/978-3-319-66700-3_5
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