{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T08:49:39Z","timestamp":1768553379904,"version":"3.49.0"},"reference-count":43,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2019,8,31]],"date-time":"2019-08-31T00:00:00Z","timestamp":1567209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Econ. Comput."],"published-print":{"date-parts":[[2019,8,31]]},"abstract":"<jats:p>\n            We consider the efficiency of taxation in congestion games with polynomial latency functions along the line of research initiated by Caragiannis et al. [\n            <jats:italic>ACM Transactions on Algorithms<\/jats:italic>\n            , 2010], who focused on both pure and mixed Nash equilibria in games with affine latencies only. By exploiting the primal-dual method [Bil\u00f2,\n            <jats:italic>Proceedings of the 10th Workshop on Approximation and Online Algorithms<\/jats:italic>\n            , 2012], we obtain interesting upper bounds with respect to a variety of different solution concepts ranging from approximate pure Nash equilibria up to approximate coarse correlated equilibria, and including also approximate one-round walks starting from the empty state. Our findings show a high beneficial effect of taxation that increases more than linearly with the degree of the latency functions. In some cases, a tight relationship with some well-studied polynomials in Combinatorics and Number Theory, such as the Touchard and the Geometric polynomials, arises. In these cases, we can also show matching lower bounds, albeit under mild assumptions; interestingly, our upper bounds are derived by exploiting the combinatorial definition of these polynomials, while our lower bounds are constructed by relying on their analytical characterization.\n          <\/jats:p>","DOI":"10.1145\/3355946","type":"journal-article","created":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T12:58:26Z","timestamp":1569329906000},"page":"1-36","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["Dynamic Taxes for Polynomial Congestion Games"],"prefix":"10.1145","volume":"7","author":[{"given":"Vittorio","family":"Bil\u00f2","sequence":"first","affiliation":[{"name":"University of Salento, Lecce, Italy"}]},{"given":"Cosimo","family":"Vinci","sequence":"additional","affiliation":[{"name":"University of L\u2019Aquila, Italy"}]}],"member":"320","published-online":{"date-parts":[[2019,9,24]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1455248.1455249"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/090748986"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/070680096"},{"key":"e_1_2_1_4_1","volume-title":"Proceedings of the 37th ACM Symposium on Theory of Computing (STOC\u201905)","author":"Awerbuch B."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2629666"},{"key":"e_1_2_1_6_1","volume-title":"Proceedings of the 10th Workshop on Approximation and Online Algorithms (WAOA\u201912)","volume":"7846","author":"Bil\u00f2 V.","year":"2012"},{"key":"e_1_2_1_7_1","unstructured":"V. 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