Abstract
Given a collection \(\mathcal{C}\) of weighted subsets of a ground set \(\mathcal{E}\), the set cover problem is to find a minimum weight subset of \(\mathcal{C}\) which covers all elements of \(\mathcal{E}\). We study a strategic game defined upon this classical optimization problem. Every element of \(\mathcal{E}\) is a player which chooses one set of \(\mathcal{C}\) where it appears. Following a public tax function, every player is charged a fraction of the weight of the set that it has selected. Our motivation is to design a tax function having the following features: it can be implemented in a distributed manner, existence of an equilibrium is guaranteed and the social cost for these equilibria is minimized.
This work is supported by French National Agency (ANR), project COCA ANR-09-JCJC-0066-01.
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Escoffier, B., Gourvès, L., Monnot, J. (2010). On the Impact of Local Taxes in a Set Cover Game. In: Patt-Shamir, B., Ekim, T. (eds) Structural Information and Communication Complexity. SIROCCO 2010. Lecture Notes in Computer Science, vol 6058. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13284-1_2
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DOI: https://doi.org/10.1007/978-3-642-13284-1_2
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