Skip to main content
SpringerLink
Log in

Some Anomalies of Farsighted Strategic Behavior

  • Published:
Theory of Computing Systems Aims and scope Submit manuscript

Abstract

We investigate the loss in optimality due to the presence of selfish players in sequential games, a relevant subclass of extensive form games with perfect information recently introduced in Paes Leme et al. (Proceedings of innovations in theoretical computer science (ITCS), ACM, New York, pp. 60–67, 2012). In such a setting, the notion of subgame perfect equilibrium is preferred to that of Nash equilibrium since it better captures the farsighted rationality of the players who can anticipate future strategic opportunities. We prove that the sequential price of anarchy, that is the worst-case ratio between the social performance at a subgame perfect equilibrium and that of the best possible solution, is exactly 3 in cut and consensus games. Moreover, we improve the known Ω(n) lower bound for unrelated scheduling to \(2^{\varOmega(\sqrt{n})}\) and refine the corresponding upper bound to 2n, where n is the number of players. Finally, we determine essentially tight bounds for fair cost sharing games by proving that the sequential price of anarchy is between n+1−H n and n. A surprising lower bound of (n+1)/2 is also determined for the singleton case.

Our results are quite interesting and counterintuitive, as they show that a farsighted behavior may lead to a worse performance with respect to a myopic one: in fact, either Nash equilibria and simple Nash rounds, consisting of a single (myopic) move per player starting from the empty state, achieve a price of anarchy which results to be lower or equivalent to the sequential price of anarchy in almost all the considered cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Aumann, R.J.: Acceptable points in general cooperative n-person games. In: Tucker, A.W., Luce, R.D. (eds.) Contributions to the Theory of Games, vol. IV. Ann. of Math. Stud., vol. 40, pp. 287–324. Princeton University Press, Princeton (1959)

    Google Scholar 

  2. Albers, S.: On the value of coordination in network design. SIAM J. Comput. 38(6), 2273–2302 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Albers, S., Lenzner, P.: On approximate Nash equilibria in network design. In: Proceedings of the 6th Workshop on Internet and Network Economics (WINE), pp. 14–25 (2010)

    Chapter  Google Scholar 

  4. Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4), 1602–1623 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 189–198 (2007)

    Google Scholar 

  6. Balcan, M.F.: Leading dynamics to good behavior. ACM SIGecom Exch. 10, 19–22 (2011)

    Article  Google Scholar 

  7. Bhalgat, A., Chakraborty, T., Khanna, S.: Approximating pure Nash equilibrium in cut, party affiliation, and satisfiability games. In: Proceedings of the 11th ACM Conference on Electronic Commerce (EC), pp. 73–82 (2010)

    Google Scholar 

  8. Bilò, V., Fanelli, A., Flammini, M., Melideo, G., Moscardelli, L.: Designing fast converging cost sharing methods for multicast transmissions. Theory Comput. Syst. 47(2), 507–530 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  9. Bilò, V., Fanelli, A., Flammini, M., Moscardelli, L.: When ignorance helps: graphical multicast cost sharing games. Theor. Comput. Sci. 411(3), 660–671 (2010)

    Article  MATH  Google Scholar 

  10. Bilò, V., Flammini, M.: Extending the notion of rationality of selfish agents: second order Nash equilibria. Theor. Comput. Sci. 412(22), 2296–2311 (2011)

    Article  MATH  Google Scholar 

  11. Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. Algorithmica 61(3), 606–637 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  12. Charikar, M., Karloff, H.J., Mathieu, C., Naor, J., Saks, M.E.: Online multicast with egalitarian cost sharing. In: Proceedings of the 20th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 70–76 (2008)

    Google Scholar 

  13. Chekuri, C., Chuzhoy, J., Lewin-Eytan, L., Naor, J., Orda, A.: Non-cooperative multicast and facility location games. IEEE J. Sel. Areas Commun. 25(6), 1193–1206 (2007)

    Article  Google Scholar 

  14. Chien, S., Sinclair, A.: Convergence to approximate Nash equilibria in congestion games. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 169–178 (2007)

    Google Scholar 

  15. Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proceedings of ACM Symposium on Theory of Computing (STOC), pp. 67–73 (2005)

    Google Scholar 

  16. Christodoulou, G., Mirrokni, V.S., Sidiropoulos, A.: Convergence and Approximation in Potential Games. Theoretical Computer Science, vol. 438, pp. 13–27 (2012)

    Google Scholar 

  17. Czumaj, A., Krysta, P., Vöcking, B.: Selfish traffic allocation for server farms. SIAM J. Comput. 39(5), 1957–1987 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  18. Deng, X., Papadimitriou, C.H.: On the complexity of cooperative solution concepts. Math. Oper. Res. 19(2), 257–266 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  19. Epstein, A., Feldman, M., Mansour, Y.: Strong equilibrium in cost sharing connection games. In: ACM Conference on Electronic Commerce (EC), pp. 84–92 (2007)

    Google Scholar 

  20. Fanelli, A., Flammini, M., Moscardelli, L.: The speed of convergence in congestion games under best-response dynamics. ACM Trans. Algorithms 8(3), 25 (2012)

    Article  MathSciNet  Google Scholar 

  21. Flammini, M., Gallotti, V., Melideo, G., Monaco, G., Moscardelli, L.: Mobile network creation games. In: Proceedings of 19th International Colloquium on Structural Information and Communication Complexity (SIROCCO), pp. 159–170 (2012)

    Chapter  Google Scholar 

  22. Fabrikant, A., Luthra, A., Maneva, E.N., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: Proceedings of the Twenty-Second ACM Symposium on Principles of Distributed Computing (PODC), pp. 347–351 (2003)

    Chapter  Google Scholar 

  23. Fanelli, A., Moscardelli, L.: On best response dynamics in weighted congestion games with polynomial delays. Distrib. Comput. 24(5), 245–254 (2011)

    Article  MATH  Google Scholar 

  24. Gourvès, L., Monnot, J.: On strong equilibria in the max cut game. In: Proceedings of the 5th Workshop on Internet and Network Economics (WINE), pp. 608–615 (2009)

    Chapter  Google Scholar 

  25. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Proceedings of Symposium on Theoretical Aspects of Computer Science (STACS). LNCS, vol. 1563, pp. 404–413. Springer, Berlin (1999)

    Google Scholar 

  26. Paes Leme, R., Syrgkanis, V., Tardos, É.: The curse of simultaneity. In: Proceedings of Innovations in Theoretical Computer Science (ITCS), pp. 60–67. ACM, New York (2012)

    Google Scholar 

  27. Paes Leme, R., Syrgkanis, V., Tardos, É.: Sequential auctions and externalities. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 869–886 (2012)

    Chapter  Google Scholar 

  28. Mirrokni, V.S., Vetta, A.: Convergence issues in competitive games. In: Proceedings of the 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problem (APPROXRANDOM). LNCS, vol. 3122, pp. 183–194. Springer, Berlin (2004)

    Chapter  Google Scholar 

  29. Nash, J.F.: Equilibrium points in n-person games. In: Proceedings of the National Academy of Sciences of the United States of America, vol. 36, pp. 48–49 (1950)

    Google Scholar 

  30. Nash, J.F.: Non-cooperative games. Ann. Math. 54(2), 286–295 (1951)

    Article  MATH  MathSciNet  Google Scholar 

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

    Book  MATH  Google Scholar 

  32. Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge (1994)

    MATH  Google Scholar 

  33. Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)

    Article  MathSciNet  Google Scholar 

  34. Shapley, L.S.: The value of n-person games. In: Contributions to the Theory of Games, pp. 31–40. Princeton University Press, Princeton (1953)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Provinciale Lecce-Arnesano, P.O. Box 193, 73100, Lecce, Italy

    Vittorio Bilò

  2. Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università di L’Aquila, Via Vetoio, Loc. Coppito, 67100, L’Aquila, Italy

    Michele Flammini & Gianpiero Monaco

  3. Gran Sasso Science Institute, viale Francesco Crispi, 67100, L’Aquila, Italy

    Michele Flammini

  4. Dipartimento di Economia, Università di Chieti-Pescara, Viale Pindaro 42, 65127, Pescara, Italy

    Luca Moscardelli

Authors
  1. Vittorio Bilò
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michele Flammini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gianpiero Monaco
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Luca Moscardelli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luca Moscardelli.

Additional information

A preliminary version of this work has been published in the proceedings of the 10th Workshop on Approximation and Online Algorithms (WAOA 2012). This research was partially supported by the PRIN 2010–2011 research project ARS TechnoMedia (Algorithmics for Social Technological Networks), funded by the Italian Ministry of Education, University and Research.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bilò, V., Flammini, M., Monaco, G. et al. Some Anomalies of Farsighted Strategic Behavior. Theory Comput Syst 56, 156–180 (2015). https://doi.org/10.1007/s00224-013-9529-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00224-013-9529-1

Keywords

Search

Navigation