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On Equilibria for ADM Minimization Games

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Abstract

In the ADM minimization problem the input is a set of arcs along a directed ring. The input arcs need to be partitioned into non-overlapping chains and cycles so as to minimize the total number of endpoints, where a k-arc cycle contributes k endpoints and a k-arc chain contains k+1 endpoints. We study ADM minimization problem both as non-cooperative and cooperative games. In these games each arc corresponds to a player, and the players share the cost of the ADM switches. We consider two cost allocation models, a model which was considered by Flammini et al., and a new cost allocation model, which is inspired by congestion games. We compare the price of anarchy and price of stability in the two cost allocation models, as well as the strong price of anarchy and the strong price of stability.

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa, 31905, Haifa, Israel

    Leah Epstein

  2. Faculty of Industrial Engineering and Management, The Technion, 32000, Haifa, Israel

    Asaf Levin

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  1. Leah Epstein
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  2. Asaf Levin
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Correspondence to Leah Epstein.

Additional information

An extended abstract of this work appeared in the proceedings of the second International Symposium on Algorithmic Game Theory (SAGT2009), pp. 347–358.

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Epstein, L., Levin, A. On Equilibria for ADM Minimization Games. Algorithmica 63, 246–273 (2012). https://doi.org/10.1007/s00453-011-9530-5

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