Dynamic Games and Applications

, Volume 5, Issue 1, pp 26–64 | Cite as

Adversarial Behavior in Network Games

  • Anil Kumar Chorppath
  • Tansu Alpcan
  • Holger Boche


This paper studies the effects of and countermeasures against adversarial behavior in network resource allocation mechanisms such as auctions and pricing schemes. It models the heterogeneous behavior of users, which ranges from altruistic to selfish and to malicious, within the analytical framework of game theory. A mechanism design approach is adopted to quantify the effect of adversarial behavior, which ranges from extreme selfishness to destructive maliciousness. First, the well-known result on the Vicrey–Clarke–Groves (VCG) mechanism losing its efficiency property in the presence of malicious users is extended to the case of divisible resource allocation to motivate the need to quantify the effect of malicious behavior. Then, the Price of Malice of the VCG mechanism and of some other network mechanisms are derived. In this context, the dynamics and convergence properties of an iterative distributed pricing algorithm are analyzed. The resistance of a mechanism to collusions is investigated next, and the effect of collusion of some malicious users is quantified. Subsequently, the assumption that the malicious user has information about the utility function of selfish users is relaxed, and a regression-based iterative learning scheme is presented and applied to both pricing and auction mechanisms. Differentiated pricing as a method to counter adversarial behaviors is proposed and briefly discussed. The results obtained are illustrated with numerical examples and simulations.


Adversarial behavior Mechanism design Game theory  Detection and counter measures Collusion Interference management 



This work has been supported in part by Deutsche Telekom Laboratories, Berlin, Germany and by the COIN project by German National Science Foundation (DFG) BO 1734/24-1. A conference version of this work has appeared in proceedings of Gamecomm 2011, May 2011, Cachen, France.


  1. 1.
    Alpcan T, Başar T (2005) A utility-based congestion control scheme for internet-style networks with delay. IEEE Trans Netw 13(6):1261–1274CrossRefGoogle Scholar
  2. 2.
    Alpcan T, Basar T (2010) Network security: a decision and game theoretic approach. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  3. 3.
    Alpcan T, Boche H, Honig M, Poor HV (eds) (2013) Mechanisms and games for dynamic spectrum allocation. Cambridge University Press, CambridgeGoogle Scholar
  4. 4.
    Alpcan T, Pavel L (2009) Nash equilibrium design and optimization. In: Proceedings of international conference on game theory for networks (GameNets 2009), IstanbulGoogle Scholar
  5. 5.
    Altman E, Kameda H, Hayel Y (2011) Revisiting collusion in routing games: a load balancing problem. In: 5th International conference on network games, control and optimization (NetGCooP), Oct 2011, pp 1–6Google Scholar
  6. 6.
    Aryal G, Gabrielli MF (2012) Estimating revenue under collusion-proof auctions. Soc Sci Res Network. doi: 10.2139/ssrn.2173232
  7. 7.
    Aumann RJ (1987) Correlated equilibrium as an expression of bayesian rationality. Econometrica 55(1): 1–18Google Scholar
  8. 8.
    Avrachenkov K, Altman E, Garnaev A (2007) A jamming game in wireless networks with transmission cost. Lect Notes Comput Sci 4465:1–12CrossRefGoogle Scholar
  9. 9.
    Azad AP, Altman E, Azouzi RE (2008) From altruism to non-cooperation in routing games, CoRR, arXiv:0808.4079
  10. 10.
    Azad AP, Musacchio J (2011) Unilateral altruism in network routing games with atomic players. CoRR. arXiv:1108.1233
  11. 11.
    Babaioff M, Kleinberg R, Papadimitriou CH (2007) Congestion games with malicious players. In: Proceedings of the 8th ACM conference on electronic commerce, San Diego, pp 103–112Google Scholar
  12. 12.
    Balcan M-F, Blum A, Hartline JD, Mansour Y (2008) Reducing mechanism design to algorithm design via machine learning. J Comput Syst Sci 74:1245–1270.
  13. 13.
    Başar T, Olsder GJ (1999) Dynamic noncooperative game theory, 2nd edn. SIAM, PhiladelphiazbMATHGoogle Scholar
  14. 14.
    Bertsekas DP, Tsitsiklis J (1997) Parallel and distributed computation: numerical methods, 1st edn. Athena Scientific, BelmontGoogle Scholar
  15. 15.
    Boche H, Naik S, Alpcan T (2010) A unified mechanism design framework for networked systems. arXiv:1009.0377[cs.GT], Tech. Rep.
  16. 16.
    Brandt F, Sandholm T, Shoham Y (2007) Spiteful bidding in sealed-bid auctions. In: IJCAI’07 proceedings of the 20th international joint conference on artifical intelligence, Hyderabad, pp 1207–1214Google Scholar
  17. 17.
    Chen PA, Kempe D (2008) Altruism, selfishness, and spite in traffic routing. In: Electronic commerce, EC08, Chicago, pp 8–125Google Scholar
  18. 18.
    Chen J, Micali S (2012) Collusive dominant-strategy truthfulness. J Econ Theory 147(3):1300–1312.
  19. 19.
    Chorppath AK, Alpcan T (2011) Learning user preferences in mechanism design. In: Proceedings of 50th IEEE conference on decision and control and european control conference, OrlandoGoogle Scholar
  20. 20.
    Chorppath AK, Alpcan T, Boche H (2011) Pricing mechanisms for multi-carrier wireless systems. In: Proceedings of IEEE international symposium on dynamic spectrum access networks (DySPAN), AachenGoogle Scholar
  21. 21.
    Chorppath AK, Alpcan T, Boche H (2013) Games and mechanisms for networked systems: incentives and algorithms. In: Mechanisms and games for dynamic spectrum allocation. Cambridge University Press, CambridgeGoogle Scholar
  22. 22.
    Chorppath AK, Bhashyam S, Sundaresan R (2011) A convex optimization framework for almost budget balanced allocation of a divisible good. IEEE Trans Autom Sci Eng 8:520–531CrossRefGoogle Scholar
  23. 23.
    Harsanyi JC (1967) Games with incomplete information played by ‘Bayesian’ players. Manag Sci Theory Ser 14(3):159–182CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Hayrapetyan A, Tardos E, Wexler T (2006) The effect of collusion in congestion games. In: Proceedings of the thirty-eighth annual ACM symposium on theory of computing, ser. STOC ’06. ACM, New York, pp 89–98. doi: 10.1145/1132516.1132529
  25. 25.
    Huang J, Berry R, Honig M (2006) Auction-based spectrum sharing. ACM Mob Netw Appl J 24(5): 405–418Google Scholar
  26. 26.
    Johari R, Mannor S, Tsitsiklis J (2005) Efficiency loss in a network resource allocation game: the case of elastic supply. IEEE Trans Autom Control 50(11):1712–1724CrossRefMathSciNetGoogle Scholar
  27. 27.
    Kelly FP, Maulloo AK, Tan D (1998) Rate control in communication networks: shadow prices, proportional fairness and stability. J Oper Res Soc 49:237–252CrossRefzbMATHGoogle Scholar
  28. 28.
    Koutsoupias E, Papadimitriou C (1999) Worst-case equilibria. Lect Notes Comput Sci 1563:404–413CrossRefMathSciNetGoogle Scholar
  29. 29.
    Krishna V (2010) Auction theory, 2nd edn. Academic Press, LondonGoogle Scholar
  30. 30.
    Maheswaran RT, Basar T (2004) Social welfare of selfish agents: motivating efficiency for divisible resources. In: 43rd IEEE conference on decision and control (CDC), Paradise Island, Bahamas, pp 1550–1555Google Scholar
  31. 31.
    Micali S, Valiant P (2008) Revenue in truly combinatorial auctions and adversarial mechanism design. MIT Comput Sci Artif Intell Lab Tech Rep.
  32. 32.
    Moscibroda T, Schmid S, Wattenhofer R (2006) When selfish meets evil: byzantine players in a virus inoculation game. In: Proceedings of the twenty-fifth annual ACM symposium on principles of distributed computing, DenverGoogle Scholar
  33. 33.
    Moulin H, Shenker S (2001) Strategyproof sharing of submodular costs: budget balance versus efficiency. J Econ Theory 18(3):511–533CrossRefzbMATHMathSciNetGoogle Scholar
  34. 34.
    Netzer N (2012) An externality-robust auction. Working paperGoogle Scholar
  35. 35.
    Rasmussen CE, Williams CKI (2005) Gaussian processes for machine learning (adaptive computation and machine learning). The MIT Press.
  36. 36.
    Rosen JB (1965) Existence and uniqueness of equilibrium points for concave N-person games. Econometrica 33(3):520–534CrossRefzbMATHMathSciNetGoogle Scholar
  37. 37.
    Roth A (2008) The price of malice in linear congestion games. In: WINE ’08: proceedings of the 4th international workshop on internet and network economics, pp 118–125Google Scholar
  38. 38.
    Roughgarden T (2002) The price of anarchy is independent of the network topology. In: Proceedings of the 34th annual ACM symposium on the theory of computingGoogle Scholar
  39. 39.
    Srikant R (2004) The mathematics of internet congestion control, ser. systems & control: foundations & applications. Birkhauser, BostonCrossRefGoogle Scholar
  40. 40.
    Steiglitz K, Morgan J, Reis G (2003) The spite motive and equilibrium behavior in auctions. Contrib Econ Anal Policy 2(5):1102–1127Google Scholar
  41. 41.
    Theodorakopoulos S, Baras JS (2008) Game theoretic modeling of malicious users in collaborative networks. IEEE J Sel Areas Commun 26(7):1317–1327Google Scholar
  42. 42.
    Vickrey W (1961) Counterspeculation, auctions and competitive sealed tenders. J Finance 16(1):8–37CrossRefGoogle Scholar
  43. 43.
    Xu W, Trappe W, Zhang Y, Wood T (2005) The feasibility of launching and detecting jamming attacks in wireless networks. In: MobiHoc ’05 proceedings of the 6th ACM international symposium on Mobile Ad Hoc networking and computing, pp 47–56Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Anil Kumar Chorppath
    • 1
  • Tansu Alpcan
    • 2
  • Holger Boche
    • 1
  1. 1.Technical University of MunichMunichGermany
  2. 2.The University of MelbourneMelbourneAustralia

Personalised recommendations