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An Algorithm to Compute the Nucleolus of Shortest Path Games

Abstract : We study a type of cooperative games introduced in [9] 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.
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Submitted on : Wednesday, December 16, 2020 - 11:17:27 AM
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Mourad Baïou, Francisco Barahona. An Algorithm to Compute the Nucleolus of Shortest Path Games. Algorithmica, Springer Verlag, 2019, 81 (8), pp.3099-3113. ⟨10.1007/s00453-019-00574-9⟩. ⟨hal-02348972⟩

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