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Assignment Games with Conflicts: Robust Price of Anarchy and Convergence Results via Semi-Smoothness

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Abstract

We study assignment games in which jobs select machines, and in which certain pairs of jobs may conflict, which is to say they may incur an additional cost when they are both assigned to the same machine, beyond that associated with the increase in load. Questions regarding such interactions apply beyond allocating jobs to machines: when people in a social network choose to align themselves with a group or party, they typically do so based upon not only the inherent quality of that group, but also who amongst their friends (or enemies) chooses that group as well. We show how semi-smoothness, a recently introduced generalization of smoothness, is necessary to find tight bounds on the robust price of anarchy, and thus on the quality of correlated and Nash equilibria, for several natural job-assignment games with interacting jobs. For most cases, our bounds on the robust price of anarchy are either exactly 2 or approach 2. We also prove new convergence results implied by semi-smoothness for our games. Finally we consider coalitional deviations, and prove results about the existence and quality of strong equilibrium.

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References

  1. Augustine, J., Chen, N., Elkind, E., Fanelli, A., Gravin, N., Shiryaev, D.: Dynamics of profit-sharing games. In: IJCAI, pp. 37–42 (2011)

  2. Awerbuch, B., Azar, Y., Epstein, A., Mirrkoni, V.S., Skopalik, A.: Fast convergence to nearly optimal solutions in potential games. In: Proceedings of EC, pp. 264–273 (2008)

  3. Bachrach, Y., Syrgkanis, V., Tardos, É., Vojnović, M.: Strong Price of Anarchy, Utility Games, and Coalitional Dynamics. In: Proceedings of SAGT (2014)

  4. Bhalgat, A., Chakraborty, T., Khanna, S.: Approximating pure nash equilibrium in cut, party affiliation, and satisfiability games. In: Proceedings of EC, pp. 73–82 (2010)

  5. Blum, A., Hajiaghayi, M., Ligett, K., Roth, A.: Regret minimization and the price of total anarchy. In: Proceedings of STOC, pp. 373–382 (2008)

  6. Caragiannis, I., Flammini, M., Kaklamansis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. In: Proceedings of ICALP, pp. 311–322 (2006)

  7. Caragiannis, I., Kaklamansis, C., Kanellopoulos, P., Kyropoulou, M., Lucier, B., Leme, R.P., Tardos, É.: Bounding the inefficiency of outcomes in generalized second price auctions. J. Econ. Theory 156, 343–388 (2015)

  8. Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proceedings of STOC, pp. 67–73 (2005)

  9. Christodoulou, G., Mirrokni, V.S., Sidiropoulos, A.: Convergence and approximation in potential games. In: Proceedings of STACS, pp. 349–360 (2006)

  10. Fanelli, A., Flammini, M., Moscardelli, L.: The speed of convergence in congestion games under best-response dynamics. In: Proceedings of ICALP, pp. 796–807 (2008)

  11. Fanelli, A., Moscardelli, L.: On best response dynamics in weighted congestion games with polynomial delays. In: Proceedings of WINE, pp. 55–66 (2009)

  12. Feldman, M., Lewin-Eytan, L., Naor, J.S.: Hedonic clustering games. In: Proceedings of SPAA, pp. 267–276 (2012)

  13. Goemans, M.X., Li, L., Mirrokni, V.S., Thottan, M.: Market sharing games applied to content distribution in ad-hoc networks. In: Proceedings of JSAC, vol. 24, no. 5, pp. 1020–1033 (2006)

  14. Gourvès, L., Monnot, J.: On strong equilibria in the max cut game. In: Proceedings of WINE, pp. 608–615 (2009)

  15. Gourvès, L., Monnot, J.: The max k-cut game and its strong equilibria. In: Proceedings of TAMC, pp. 234–246 (2010)

  16. Hoefer, M.: Cost Sharing and Clustering under Distributed Competition. PhD Thesis, Universität Konstanz (2007)

  17. Jackson, M.O., Yariv, L.: Diffusion of behavior and equilibrium properties in network games. Am. Econ. Rev. 97(2), 92–98 (2007)

    Article  Google Scholar 

  18. Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: KDD ’03, pp 137–146

  19. Kleinberg, J.: Cascading behavior in networks: algorithmic and economic issues. In: Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V. (eds.) Algorithmic Game Theory, pp. 613–632 (2007)

  20. Kothari, A., Suri, S., Tóth, C.D., Zhou, Y.: Congestion games, load balancing, and the price of anarchy. In: Proceedings of CAAN, pp. 13–27 (2004)

  21. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Proceedings of STACS, pp. 404–413 (1999)

  22. Lucier, B., Leme, R.P.: GSP auctions with correlated types. In: Proceedings of EC, pp. 71–80 (2011)

  23. Mirrokni, V.S., Vetta, A.: Convergence issues in competitive games. In: Proceedings of RANDOM-APPROX, pp. 183–194 (2014)

  24. Monderer, D., Shapley, L.S.: Potential games. Games Econ. Behav. 14(1), 124–143 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  25. Morris, S.: Contagion. Rev. Econ. Stud. 67(1), 57–78 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  26. Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V. (eds.): Algorithmic Game Theory. Cambridge University Press (2007)

  27. Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: Proceedings of STOC, pp. 513–522 (2009)

  28. Roughgarden, T., Schoppmann, F.: Local smoothness and the price of anarchy in atomic splittable congestion games. In: Proceedings of SODA, pp. 255–267 (2011)

  29. Suri, S., Tóth, C.D., Zhou, Y.: Selfish load balancing and atomic congestion games. Algorithmica 47(1), 79–96 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  30. Vöcking, B.: Selfish load balancing. In: Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V. (eds.) Algorithmic Game Theory, pp. 517–542 (2007)

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Acknowledgments

This work was supported in part by NSF grants CCF-0914782, CCF-1101495, and CNS-1017932. We thank Carlos Varela for illuminating discussions on the subject of job assignment.

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Authors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Elliot Anshelevich & John Postl

  2. Oberlin College, Oberlin, OH, 44074, USA

    Tom Wexler

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  1. Elliot Anshelevich
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  2. John Postl
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  3. Tom Wexler
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Correspondence to Elliot Anshelevich.

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Anshelevich, E., Postl, J. & Wexler, T. Assignment Games with Conflicts: Robust Price of Anarchy and Convergence Results via Semi-Smoothness. Theory Comput Syst 59, 440–475 (2016). https://doi.org/10.1007/s00224-015-9646-0

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  • DOI: https://doi.org/10.1007/s00224-015-9646-0

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