Abstract
We investigate the approximation ratio of the solutions achieved after a one-round walk in linear congestion games. We consider the social functions \({\mathrm{S}\textsc{um}}\), defined as the sum of the players’ costs, and \({\mathrm{M}\textsc{ax}}\), defined as the maximum cost per player, as a measure of the quality of a given solution. For the social function \({\mathrm{S}\textsc{um}}\) and one-round walks starting from the empty strategy profile, we close the gap between the upper bound of \(2+\sqrt{5}\approx 4.24\) given in [8] and the lower bound of 4 derived in [4] by providing a matching lower bound whose construction and analysis require non-trivial arguments. For the social function \({\mathrm{M}\textsc{ax}}\), for which, to the best of our knowledge, no results were known prior to this work, we show an approximation ratio of \(\Theta(\sqrt[4]{n^3})\) (resp. \(\Theta(n\sqrt{n})\)), where n is the number of players, for one-round walks starting from the empty (resp. an arbitrary) strategy profile.
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Bilò, V., Fanelli, A., Flammini, M., Moscardelli, L. (2009). Performances of One-Round Walks in Linear Congestion Games. In: Mavronicolas, M., Papadopoulou, V.G. (eds) Algorithmic Game Theory. SAGT 2009. Lecture Notes in Computer Science, vol 5814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04645-2_28
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DOI: https://doi.org/10.1007/978-3-642-04645-2_28
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