Abstract
One of the main results shown through Roughgarden’s notions of smooth games and robust price of anarchy is that, for any sum-bounded utilitarian social function, the worst-case price of anarchy of coarse correlated equilibria coincides with that of pure Nash equilibria in the class of weighted congestion games with non-negative and non-decreasing latency functions and that such a value can always be derived through the, so called, smoothness argument. We significantly extend this result by proving that, for a variety of (even non-sum-bounded) utilitarian and egalitarian social functions and for a broad generalization of the class of weighted congestion games with non-negative (and possibly decreasing) latency functions, the worst-case price of anarchy of \(\epsilon \)-approximate coarse correlated equilibria still coincides with that of \(\epsilon \)-approximate pure Nash equilibria, for any \(\epsilon \ge 0\). As a byproduct of our proof, it also follows that such a value can always be determined by making use of the primal-dual method we introduced in a previous work.
This work was partially supported by the PRIN 2010–2011 research project ARS TechnoMedia: “Algorithmics for Social Technological Networks” funded by the Italian Ministry of University.
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Bilò, V. (2016). On the Robustness of the Approximate Price of Anarchy in Generalized Congestion Games. In: Gairing, M., Savani, R. (eds) Algorithmic Game Theory. SAGT 2016. Lecture Notes in Computer Science(), vol 9928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53354-3_8
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