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Adversarial Behavior in Network Games

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Abstract

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.

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References

  1. Alpcan T, Başar T (2005) A utility-based congestion control scheme for internet-style networks with delay. IEEE Trans Netw 13(6):1261–1274

    Article  Google Scholar 

  2. Alpcan T, Basar T (2010) Network security: a decision and game theoretic approach. Cambridge University Press, Cambridge

    Book  Google Scholar 

  3. Alpcan T, Boche H, Honig M, Poor HV (eds) (2013) Mechanisms and games for dynamic spectrum allocation. Cambridge University Press, Cambridge

    Google Scholar 

  4. Alpcan T, Pavel L (2009) Nash equilibrium design and optimization. In: Proceedings of international conference on game theory for networks (GameNets 2009), Istanbul

  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 1–6

  6. Aryal G, Gabrielli MF (2012) Estimating revenue under collusion-proof auctions. Soc Sci Res Network. doi:10.2139/ssrn.2173232

  7. Aumann RJ (1987) Correlated equilibrium as an expression of bayesian rationality. Econometrica 55(1): 1–18

  8. Avrachenkov K, Altman E, Garnaev A (2007) A jamming game in wireless networks with transmission cost. Lect Notes Comput Sci 4465:1–12

    Article  Google Scholar 

  9. Azad AP, Altman E, Azouzi RE (2008) From altruism to non-cooperation in routing games, CoRR, arXiv:0808.4079

  10. Azad AP, Musacchio J (2011) Unilateral altruism in network routing games with atomic players. CoRR. arXiv:1108.1233

  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 103–112

  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. http://portal.acm.org/citation.cfm?id=1460945.1461324

  13. Başar T, Olsder GJ (1999) Dynamic noncooperative game theory, 2nd edn. SIAM, Philadelphia

    MATH  Google Scholar 

  14. Bertsekas DP, Tsitsiklis J (1997) Parallel and distributed computation: numerical methods, 1st edn. Athena Scientific, Belmont

    Google Scholar 

  15. Boche H, Naik S, Alpcan T (2010) A unified mechanism design framework for networked systems. arXiv:1009.0377[cs.GT], Tech. Rep.

  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 1207–1214

  17. Chen PA, Kempe D (2008) Altruism, selfishness, and spite in traffic routing. In: Electronic commerce, EC08, Chicago, pp 8–125

  18. Chen J, Micali S (2012) Collusive dominant-strategy truthfulness. J Econ Theory 147(3):1300–1312. http://www.sciencedirect.com/science/article/pii/S0022053112000221

  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, Orlando

  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), Aachen

  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, Cambridge

  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 8:520–531

    Article  Google Scholar 

  23. Harsanyi JC (1967) Games with incomplete information played by ‘Bayesian’ players. Manag Sci Theory Ser 14(3):159–182

    Article  MATH  MathSciNet  Google Scholar 

  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. Huang J, Berry R, Honig M (2006) Auction-based spectrum sharing. ACM Mob Netw Appl J 24(5): 405–418

  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):1712–1724

    Article  MathSciNet  Google Scholar 

  27. Kelly FP, Maulloo AK, Tan D (1998) Rate control in communication networks: shadow prices, proportional fairness and stability. J Oper Res Soc 49:237–252

    Article  MATH  Google Scholar 

  28. Koutsoupias E, Papadimitriou C (1999) Worst-case equilibria. Lect Notes Comput Sci 1563:404–413

    Article  MathSciNet  Google Scholar 

  29. Krishna V (2010) Auction theory, 2nd edn. Academic Press, London

    Google Scholar 

  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 1550–1555

  31. Micali S, Valiant P (2008) Revenue in truly combinatorial auctions and adversarial mechanism design. MIT Comput Sci Artif Intell Lab Tech Rep. http://dspace.mit.edu/handle/1721.1/41872

  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, Denver

  33. Moulin H, Shenker S (2001) Strategyproof sharing of submodular costs: budget balance versus efficiency. J Econ Theory 18(3):511–533

    Article  MATH  MathSciNet  Google Scholar 

  34. Netzer N (2012) An externality-robust auction. Working paper

  35. Rasmussen CE, Williams CKI (2005) Gaussian processes for machine learning (adaptive computation and machine learning). The MIT Press. http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20&path=ASIN/026218253X

  36. Rosen JB (1965) Existence and uniqueness of equilibrium points for concave N-person games. Econometrica 33(3):520–534

    Article  MATH  MathSciNet  Google Scholar 

  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 118–125

  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 computing

  39. Srikant R (2004) The mathematics of internet congestion control, ser. systems & control: foundations & applications. Birkhauser, Boston

    Book  Google Scholar 

  40. Steiglitz K, Morgan J, Reis G (2003) The spite motive and equilibrium behavior in auctions. Contrib Econ Anal Policy 2(5):1102–1127

    Google Scholar 

  41. Theodorakopoulos S, Baras JS (2008) Game theoretic modeling of malicious users in collaborative networks. IEEE J Sel Areas Commun 26(7):1317–1327

  42. Vickrey W (1961) Counterspeculation, auctions and competitive sealed tenders. J Finance 16(1):8–37

    Article  Google Scholar 

  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 47–56

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Acknowledgments

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.

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Correspondence to Anil Kumar Chorppath.

Appendix

Appendix

Definitions:

The properties of mechanisms considered in this paper can be formally defined as follows.

Definition 11.1

Efficiency: Efficient mechanisms maximize designer objective, i.e., they solve the problem \(\max _x V(x,U_i(x),c_i(x)).\)

Definition 11.2

Nash equilibrium: The strategy profile \( x^*=[x^*_1,\ldots ,x^*_N]\) is in Nash equilibrium if the cost of each player is minimized at the equilibrium given the best strategies of other players.

$$\begin{aligned} J_i(x^*_i,x^*_{-i}) \le J_i(x_i,x^*_{-i}) , \forall i\in \mathcal A , x_i \in \mathcal X_i \end{aligned}$$

Definition 11.3

Dominant strategy equilibrium: The strategy profile \(\tilde{x}=[\tilde{x}_1,\ldots ,\tilde{x}_N]\) is in dominant strategy equilibrium if the cost of each player is minimized at the equilibrium irrespective of the strategies of other players.

$$\begin{aligned} J_i(\tilde{x_i},x_{-i}) \le J_i({x}_i,x_{-i}) , \forall i\in \mathcal A , x_i \in \mathcal X_i,x_{-i} \in \mathcal X_{-i} \end{aligned}$$

Definition 11.4

Strategy-proofness or dominant strategy incentive compatibility: If the players do not gain anything by reporting a value other than their true value in the dominant strategy equilibrium, i.e.,

$$\begin{aligned} J_i(x^t_i,x_{-i}) \le J_i(x'_i,x_{-i} ) , \forall i\in \mathcal A ,x_i \in \mathcal X_i,x_{-i} \in \mathcal X_{-i}, \end{aligned}$$

where \(x^t\) is the original value vector, and \(x'\) is the “misrepresented” value or action, then the mechanism is strategy-proof.

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Chorppath, A.K., Alpcan, T. & Boche, H. Adversarial Behavior in Network Games. Dyn Games Appl 5, 26–64 (2015). https://doi.org/10.1007/s13235-014-0120-4

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