The minimum cost shortest-path tree game

F. Fernández () and J. Puerto ()

Annals of Operations Research, 2012, vol. 199, issue 1, 23-32

Abstract: A minimum cost shortest-path tree is a tree that connects the source with every node of the network by a shortest path such that the sum of the cost (as a proxy for length) of all arcs is minimum. In this paper, we adapt the algorithm of Hansen and Zheng (Discrete Appl. Math. 65:275–284, 1996 ) to the case of acyclic directed graphs to find a minimum cost shortest-path tree in order to be applied to the cost allocation problem associated with a cooperative minimum cost shortest-path tree game. In addition, we analyze a non-cooperative game based on the connection problem that arises in the above situation. We prove that the cost allocation given by an ‘à la’ Bird rule provides a core solution in the former game and that the strategies that induce those payoffs in the latter game are Nash equilibrium. Copyright Springer Science+Business Media, LLC 2012

Keywords: Operations research games; Core solution; Nash equilibrium (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10479-011-1043-8

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