{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T08:19:41Z","timestamp":1768551581942,"version":"3.49.0"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2018,12,13]],"date-time":"2018-12-13T00:00:00Z","timestamp":1544659200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Theory Comput Syst"],"published-print":{"date-parts":[[2019,8]]},"DOI":"10.1007\/s00224-018-9902-1","type":"journal-article","created":{"date-parts":[[2018,12,13]],"date-time":"2018-12-13T02:33:51Z","timestamp":1544668431000},"page":"1228-1249","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["On Stackelberg Strategies in Affine Congestion Games"],"prefix":"10.1007","volume":"63","author":[{"given":"Vittorio","family":"Bil\u00f2","sequence":"first","affiliation":[]},{"given":"Cosimo","family":"Vinci","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,12,13]]},"reference":[{"issue":"5","key":"9902_CR1","doi-asserted-by":"publisher","first-page":"1211","DOI":"10.1137\/090748986","volume":"40","author":"S Aland","year":"2011","unstructured":"Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F.: Exact price of anarchy for polynomial congestion games. SIAM J. Comput. 40(5), 1211\u20131233 (2011)","journal-title":"SIAM J. Comput."},{"issue":"4","key":"9902_CR2","doi-asserted-by":"publisher","first-page":"1602","DOI":"10.1137\/070680096","volume":"38","author":"E Anshelevich","year":"2008","unstructured":"Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4), 1602\u20131623 (2008)","journal-title":"SIAM J. Comput."},{"key":"9902_CR3","doi-asserted-by":"crossref","unstructured":"Awerbuch, B., Azar, Y., Epstein, L.: The price of routing unsplittable flow. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC), pp. 57\u201366. ACM Press (2005)","DOI":"10.1145\/1060590.1060599"},{"issue":"4","key":"9902_CR4","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1145\/2629666","volume":"2","author":"K Bhawalkar","year":"2014","unstructured":"Bhawalkar, K., Gairing, M., Roughgarden, T.: Weighted congestion games: price of anarchy, universal worst-case examples, and tightness. ACM Trans. Econ. Comput. 2(4), 14 (2014)","journal-title":"ACM Trans. Econ. Comput."},{"issue":"5","key":"9902_CR5","doi-asserted-by":"publisher","first-page":"1288","DOI":"10.1007\/s00224-017-9826-1","volume":"62","author":"V Bil\u00f2","year":"2018","unstructured":"Bil\u00f2, V.: A unifying tool for bounding the quality of non-cooperative solutions in weighted congestion games. Theory Comput. Syst. 62(5), 1288\u20131317 (2018)","journal-title":"Theory Comput. Syst."},{"key":"9902_CR6","doi-asserted-by":"crossref","unstructured":"Bil\u00f2, V., Vinci, C.: On Stackelberg strategies in affine congestion games. In: Proceedings of the 11th International Conference on Web and Internet Economics (WINE) LNCS 9470, pp. 132\u2013145. Springer (2015)","DOI":"10.1007\/978-3-662-48995-6_10"},{"key":"9902_CR7","doi-asserted-by":"crossref","unstructured":"Bil\u00f2, V., Vinci, C.: Dynamic taxes for polynomial congestion games. In: Proceedings of the 17th ACM Conference on Economics and Computation (EC), pp. 839\u2013856. ACM Press (2016)","DOI":"10.1145\/2940716.2940750"},{"issue":"3","key":"9902_CR8","doi-asserted-by":"publisher","first-page":"606","DOI":"10.1007\/s00453-010-9427-8","volume":"61","author":"I Caragiannis","year":"2011","unstructured":"Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. Algorithmica 61(3), 606\u2013637 (2011)","journal-title":"Algorithmica"},{"issue":"1","key":"9902_CR9","doi-asserted-by":"publisher","first-page":"13:1","DOI":"10.1145\/1868237.1868251","volume":"7","author":"I Caragiannis","year":"2010","unstructured":"Caragiannis, I., Kaklamanis, C., Kanellopoulos, P.: Taxes for linear atomic congestion games. ACM Trans. Algorithms 7(1), 13:1\u201313:31 (2010)","journal-title":"ACM Trans. Algorithms"},{"key":"9902_CR10","doi-asserted-by":"crossref","unstructured":"Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC), pp. 67\u201373. ACM Press (2005)","DOI":"10.1145\/1060590.1060600"},{"issue":"36","key":"9902_CR11","doi-asserted-by":"publisher","first-page":"3327","DOI":"10.1016\/j.tcs.2009.01.005","volume":"410","author":"G Christodoulou","year":"2009","unstructured":"Christodoulou, G., Koutsoupias, E., Nanavati, A.: Coordination mechanisms. Theor. Comput. Sci. 410(36), 3327\u20133336 (2009)","journal-title":"Theor. Comput. Sci."},{"key":"9902_CR12","doi-asserted-by":"crossref","unstructured":"Correa, J.R., Stier Moses, N.E.: Stackelberg Routing in Atomic Network Games. Technical Report DRO-2007-03 Columbia Business School (2007)","DOI":"10.2139\/ssrn.987115"},{"issue":"1","key":"9902_CR13","first-page":"218","volume":"47","author":"D Fotakis","year":"2010","unstructured":"Fotakis, D.: Stackelberg strategies for atomic congestion games. Theor. Comput. Sci. 47(1), 218\u2013249 (2010)","journal-title":"Theor. Comput. Sci."},{"issue":"7","key":"9902_CR14","doi-asserted-by":"publisher","first-page":"1199","DOI":"10.1016\/j.jcss.2008.07.001","volume":"74","author":"M Gairing","year":"2008","unstructured":"Gairing, M., L\u00fccking, T., Mavronicolas, M., Monien, B., Rode, M.: Nash equilibria in discrete routing games with convex latency functions. J. Comput. Syst. Sci. 74(7), 1199\u20131225 (2008)","journal-title":"J. Comput. Syst. Sci."},{"issue":"1","key":"9902_CR15","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1007\/s00453-007-9018-5","volume":"53","author":"G Karakostas","year":"2009","unstructured":"Karakostas, G., Kolliopoulos, S.: Stackelberg strategies for selfish routing in general multicommodity networks. Algorithmica 53(1), 132\u2013153 (2009)","journal-title":"Algorithmica"},{"issue":"2","key":"9902_CR16","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.cosrev.2009.04.003","volume":"3","author":"E Koutsoupias","year":"2009","unstructured":"Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. Comput. Sci. Rev. 3(2), 65\u201369 (2009)","journal-title":"Comput. Sci. Rev."},{"key":"9902_CR17","doi-asserted-by":"crossref","unstructured":"Kumarm, V.S.A., Marathe, M.V.: Improved results for Stackelberg strategies. In: Proceedings of the 29th International Colloquium on Automata, Languages and Programming (ICALP) LNCS 2380, pp. 776\u2013787. Springer (2002)","DOI":"10.1007\/3-540-45465-9_66"},{"issue":"3","key":"9902_CR18","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/j.tcs.2008.06.045","volume":"406","author":"T L\u00fccking","year":"2008","unstructured":"L\u00fccking, T., Mavronicolas, M., Monien, B., Rode, M.: A new model for selfish routing. Theor. Comput. Sci. 406(3), 187\u2013206 (2008)","journal-title":"Theor. Comput. Sci."},{"key":"9902_CR19","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/BF01737559","volume":"2","author":"RW Rosenthal","year":"1973","unstructured":"Rosenthal, R.W: A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2, 65\u201367 (1973)","journal-title":"Int. J. Game Theory"},{"issue":"2","key":"9902_CR20","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1137\/S0097539701397059","volume":"33","author":"T Roughgarden","year":"2004","unstructured":"Roughgarden, T.: Stackelberg scheduling strategies. SIAM J. Comput. 33(2), 332\u2013350 (2004)","journal-title":"SIAM J. Comput."},{"issue":"7","key":"9902_CR21","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1145\/2209249.2209274","volume":"55","author":"T Roughgarden","year":"2012","unstructured":"Roughgarden, T.: Intrinsic robustness of the price of anarchy. Commun. ACM 55(7), 116\u2013123 (2012)","journal-title":"Commun. ACM"},{"issue":"1","key":"9902_CR22","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s00453-006-1211-4","volume":"47","author":"S Suri","year":"2007","unstructured":"Suri, S., T\u00f3th, C.D., Zhou, Y.: Selfish load balancing and atomic congestion games. Algorithmica 47(1), 79\u201396 (2007)","journal-title":"Algorithmica"},{"issue":"4","key":"9902_CR23","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1145\/2344422.2344426","volume":"8","author":"C Swamy","year":"2012","unstructured":"Swamy, C.: The effectiveness of Stackelberg strategies and tolls for network congestion games. ACM Trans. Algorithms 8(4), 36 (2012)","journal-title":"ACM Trans. Algorithms"}],"container-title":["Theory of Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-018-9902-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00224-018-9902-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-018-9902-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,13]],"date-time":"2019-12-13T00:10:32Z","timestamp":1576195832000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00224-018-9902-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,13]]},"references-count":23,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,8]]}},"alternative-id":["9902"],"URL":"https:\/\/doi.org\/10.1007\/s00224-018-9902-1","relation":{},"ISSN":["1432-4350","1433-0490"],"issn-type":[{"value":"1432-4350","type":"print"},{"value":"1433-0490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,13]]},"assertion":[{"value":"13 December 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}