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When selfish meets evil: byzantine players in a virus inoculation game

Published: 23 July 2006 Publication History

Abstract

Over the last years, game theory has provided great insights into the behavior of distributed systems by modeling the players as utility-maximizing agents. In particular, it has been shown that selfishness causes many systems to perform in a globally suboptimal fashion. Such systems are said to have a large Price of Anarchy. In this paper, we extend this active field of research by allowing some players to be malicious or Byzantine rather than selfish. We ask: What is the impact of Byzantine players on the system's efficiency compared to purely selfish environments or compared to the social optimum? In particular, we introduce the Price of Malice which captures this efficiency degradation. As an example, we analyze the Price of Malice of a game which models the containment of the spread of viruses. In this game, each node can choose whether or not to install anti-virus software. Then, a virus starts from a random node and iteratively infects all neighboring nodes which are not inoculated. We establish various results about this game. For instance, we quantify how much the presence of Byzantine players can deteriorate or---in case of highly risk-averse selfish players---improve the social welfare of the distributed system.

References

[1]
A. Aiyer, L. Alvisi, A. Clement, M. Dahlin, J.-P. Martin, and C. Porth. BAR Fault Tolerance for Cooperative Services. In Proc. 20th ACM Symposium on Operating Systems Principles (SOSP), pages 45--58, 2005.
[2]
J. Aspnes, K. Chang, and A. Yampolskiy. Inoculation Strategies for Victims of Viruses and the Sum-of-Squares Partition Problem. In Proc. 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 43--52, 2005.
[3]
N. Bailey. The Mathematical Theory of Infectious Diseases and Its Applications. Hafner Press, 1975.
[4]
D. Dolev. The Byzantine Generals Stike Again. Journal of Algorithms, 3(1):14--30, 1982.
[5]
S. Eidenbenz, V. Kumar, and S. Zust. Equilibria in Topology Control Games for Ad Hoc Networks. In Proc. Discrete Algorithms and Methods for Mobile Computing (DIALM-POMC), 2003.
[6]
K. Eliaz. Fault Tolerant Implementation. Review of Economic Studies, 69:589--610, 2002.
[7]
A. Fabrikant, A. Luthra, E. Maneva, C. H. Papadimitriou, and S. Shenker. On a Network Creation Game. In Proc. 22nd ACM Symposium on Principles of Distributed Computing (PODC), pages 347--351, New York, USA, 2003.
[8]
J. Feigenbaum, C. Papadimitriou, R. Sami, and S. Shenker. A BGP-based Mechanism for Lowest-Cost Routing. In Proc. 21st ACM Symposium on Principles of Distributed Computing (PODC), pages 173--182, 2002.
[9]
M. Fischer, N. Lynch, and M. S. Paterson. Impossibility of Distributed Consensus with one Faulty Processor. Journal of the ACM, 32(2):374--382, 1985.
[10]
C.-Y. Koo. Broadcast in Radio Networks Tolerating Byzantine Adversial Behavior. In Proc. 23rd ACM Symposium on the Principles of Distributed Computing (PODC), pages 275--282, 2004.
[11]
E. Koutsoupias and C. Papadimitriou. Worst-Case Equilibria. Lecture Notes in Computer Science, 1563:404--413, 1999.
[12]
L. Lamport, R. Shostak, and M. Pease. The Byzantine Generals Problem. ACM Trans. Program. Lang. Syst., 4(3):382--401, 1982.
[13]
D. Malkhi and M. Reiter. Byzantine Quorum Systems. Journal of Distributed Computing, 11(4):203--213, 1998.
[14]
T. Moscibroda, S. Schmid, and R. Wattenhofer. On the Topologies Created by Selfish Peers. In Proc. 25th ACM Symposium on Principles of Distributed Computing (PODC), 2006.
[15]
N. Nisan and A. Ronen. Algorithmic Mechanism Design. In Proc. 31rd ACM Symposium on Theory of Computing (STOC), pages 129--140, 1999.
[16]
M. Osborne and A. Rubinstein. A Course in Game Theory. MIT Press, 2000.
[17]
C. Papadimitriou. Algorithms, Games, and the Internet. In Proc. 33rd ACM Symposium on Theory of Computing (STOC), pages 749--753, 2001.
[18]
R. Pastor-Satorras and A. Vespiagnani. Immunization of Complex Networks. Physical Review Letter, 65, 2002.
[19]
T. Roughgarden. Stackelberg Scheduling Strategies. In Proc. 33rd ACM Symposium on Theory of Computing (STOC), pages 104--113, 2001.
[20]
T. Roughgarden. Selfish Routing and the Price of Anarchy. MIT Press, 2005.
[21]
R. Shostak, M. Pease, and L. Lamport. Reaching Agreement in the Presence of Faults. Journal of the ACM, 27(2):228--234, 1980.
[22]
T. K. Srikant and S. Toueg. Simulating Authenticated Broadcasts to Derive Simple Fault-Tolerant Algorithms. Journal of Distributed Computing, 2(2):80--94, 1987.
[23]
J. L. Welch and N. Lynch. A New Fault-Tolerant for Clock-Synchronization. Information and Communication, 77:1--36, 1988.
[24]
A. C. Yao. Protocols for Secure Computations. In Proc. 23rd Symposium on Foundations of Computer Science (FOCS), pages 160--164, 1982.

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    cover image ACM Conferences
    PODC '06: Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
    July 2006
    230 pages
    ISBN:1595933840
    DOI:10.1145/1146381
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Published: 23 July 2006

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    Author Tags

    1. byzantine nash equilibria
    2. game theory
    3. price of anarchy
    4. price of malice
    5. selfishness
    6. virus propagation

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