Abstract
In situations without central coordination, the price of anarchy relates the quality of any Nash equilibrium to the quality of a global optimum. Instead of assuming that all players choose their actions simultaneously, we consider games where players choose their actions sequentially. The sequential price of anarchy, recently introduced by Paes Leme, Syrgkanis, and Tardos [13], relates the quality of any subgame perfect equilibrium to the quality of a global optimum. The effect of sequential decision making on the quality of equilibria, depends on the specific game under consideration. We analyze the sequential price of anarchy for atomic congestion games with affine cost functions. We derive several lower and upper bounds, showing that sequential decisions mitigate the worst case outcomes known for the classical price of anarchy [2,5]. Next to tight bounds on the sequential price of anarchy, a methodological contribution of our work is, among other things, a “factor revealing” linear programming approach we use to solve the case of three players.
Research supported by CTIT (www.ctit.nl) and 3TU.AMI (www.3tu.nl), project “Mechanisms for Decentralized Service Systems”.
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References
Angelucci, A., Bilò, V., Flammini, M., Moscardelli, L.: On the Sequential Price of Anarchy of Isolation Games. In: Du, D.-Z., Zhang, G. (eds.) COCOON 2013. LNCS, vol. 7936, pp. 17–28. Springer, Heidelberg (2013)
Awerbuch, B., Azar, Y., Epstein, A.: The Price of Routing Unsplittable Flow. In: Proceedings 37th STOC, pp. 57–66 (2005)
Bilò, V., Flammini, M., Monaco, G., Moscardelli, L.: Some Anomalies of Farsighted Strategic Behavior. In: Erlebach, T., Persiano, G. (eds.) WAOA 2012. LNCS, vol. 7846, pp. 229–241. Springer, Heidelberg (2013)
Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight Bounds for Selfish and Greedy Load Balancing. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006, Part I. LNCS, vol. 4051, pp. 311–322. Springer, Heidelberg (2006)
Christodoulou, G., Koutsoupias, E.: The Price of Anarchy of Finite Congestion Games. In: Proceedings 37th STOC, pp. 67–73 (2005)
de Jong, J., Uetz, M., Wombacher, A.: Decentralized Throughput Scheduling. In: Spirakis, P.G., Serna, M. (eds.) CIAC 2013. LNCS, vol. 7878, pp. 134–145. Springer, Heidelberg (2013)
de Jong, J., Uetz, M.: The sequential price of anarchy for atomic congestion games, TR-CTIT-14-09, CTIT, University of Twente (2014)
Fotakis, D.: Stackelberg Strategies for Atomic Congestion Games. Theory of Computing Systems 47, 218–249 (2010)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
Kuhn, H.W.: Extensive Games and the Problem of Information, Contribution to the Theory of Games. Annals of Math. Studies, vol. II, 28, pp. 193–216 (1953)
Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: A New Model for Selfish Routing. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 547–558. Springer, Heidelberg (2004)
Milchtaich, I.: Crowding games are sequentially solvable. International Journal of Game Theory 27, 501–509 (1998)
Paes Leme, R., Syrgkanis, V., Tardos, É.: The Curse of Simultaneity. In: Proceedings 3rd ITCS, pp. 60–67. ACM (2012)
Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)
Roughgarden, T.: Selfish routing with atomic players. In: Proceedings 16th SODA, pp. 1184–1185 (2005)
Selten, R.: A simple model of imperfect competition, where 4 are few and 6 are many. International Journal of Game Theory 2, 141–201 (1973)
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de Jong, J., Uetz, M. (2014). The Sequential Price of Anarchy for Atomic Congestion Games. In: Liu, TY., Qi, Q., Ye, Y. (eds) Web and Internet Economics. WINE 2014. Lecture Notes in Computer Science, vol 8877. Springer, Cham. https://doi.org/10.1007/978-3-319-13129-0_35
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DOI: https://doi.org/10.1007/978-3-319-13129-0_35
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