Algorithmica

, Volume 61, Issue 2, pp 419–446 | Cite as

Topological Implications of Selfish Neighbor Selection in Unstructured Peer-to-Peer Networks

  • Thomas Moscibroda
  • Stefan Schmid
  • Roger Wattenhofer
Article

Abstract

Current peer-to-peer (P2P) systems often suffer from a large fraction of freeriders not contributing any resources to the network. Various mechanisms have been designed to overcome this problem. However, the selfish behavior of peers has aspects which go beyond resource sharing. This paper studies the effects on the topology of a P2P network if peers selfishly select the peers to connect to. In our model, a peer exploits locality properties in order to minimize the latency (or response times) of its lookup operations. At the same time, the peer aims at not having to maintain links to too many other peers in the system. By giving tight bounds on the price of anarchy, we show that the resulting topologies can be much worse than if peers collaborated. Moreover, the network may never stabilize, even in the absence of churn. Finally, we establish the complexity of Nash equilibria in our game theoretic model of P2P networks. Specifically, we prove that it is NP-hard to decide whether our game has a Nash equilibrium and can stabilize.

Keywords

Game theory Peer-to-peer Price of anarchy NP-hardness Metric spaces 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abraham, I., Malkhi, D., Dobzinski, O.: LAND: Stretch (1+e) locality aware networks for DHTs. In: Proc. 15th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 550–559 (2004) Google Scholar
  2. 2.
    Abraham, I., Badola, A., Bickson, D., Malkhi, D., Maloo, S., Ron, S.: Practical locality-awareness for large scale information sharing. In: Proc. 4th Int. Workshop on Peer-to-Peer Systems (IPTPS) (2005) Google Scholar
  3. 3.
    Adar, E., Huberman, B.A.: Free riding on Gnutella. First Monday 5(10) (2000) Google Scholar
  4. 4.
    Albers, S., Eilts, S., Even-Dar, E., Mansour, Y., Roditty, L.: On Nash equilibria for a network creation game. In: Proc. 17th ACM Symposium on Discrete Algorithms (SODA) (2006) Google Scholar
  5. 5.
    Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: Proc. 45th Symposium on Foundations of Computer Science (FOCS), pp. 295–304 (2004) Google Scholar
  6. 6.
    Austen, I.: Like a swerving commuter, a selfish router slows traffic. The New York Times (2003) Google Scholar
  7. 7.
    Axelrod, R.: The evolution of cooperation. Science 211(4489), 1390–1396 (1981) MathSciNetCrossRefGoogle Scholar
  8. 8.
    Bharambe, A.R., Herley, C., Padmanabhan, V.N.: Analyzing and improving a BitTorrent network’s performance mechanisms. In: Proc. IEEE Conference on Computer Communications (INFOCOM), pp. 36–46 (2006) Google Scholar
  9. 9.
    Chan, H.T.-H., Gupta, A., Maggs, B.M., Zhou, S.: On hierarchical routing in doubling metrics. In: Proc. 17th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 762–771 (2005) Google Scholar
  10. 10.
    Chen, H.-L., Roughgarden, T.: Network design with weighted players. In: Proc. 18th ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 29–38 (2006) Google Scholar
  11. 11.
    Cohen, B.: Incentives build robustness in BitTorrent. In: Proc. 1st Workshop on Economics of Peer-to-Peer Systems (P2PEcon) (2003) Google Scholar
  12. 12.
    Cole, R., Dodis, Y., Roughgarden, T.: How much can taxes help selfish routing? J. Comput. Syst. Sci. 72(3), 444–467 (2006) MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Cook, S.A.: The complexity of theorem-proving procedures. In: Proc. 3rd ACM Symposium on Theory of Computing (STOC), pp. 151–158 (1971) Google Scholar
  14. 14.
    Corbo, J., Parkes, D.C.: The price of selfish behavior in bilateral network formation. In: Proc. 24th ACM Symposium on Principles of Distributed Computing (PODC), pp. 99–107 (2005) Google Scholar
  15. 15.
    Demaine, E.D., Hajiaghayi, M.T., Mahini, H., Zadimoghaddam, M.: On the topologies formed by selfish peers. In: Proc. 26th Annual Symposium on Principles of Distributed Computing (PODC) (2007) Google Scholar
  16. 16.
    Demaine, E.D., Hajiaghayi, M., Mahini, H., Zadimoghaddam, M.: The price of anarchy in cooperative network creation games. In: Proc. 26th International Symposium on Theoretical Aspects of Computer Science (STACS) (2009) Google Scholar
  17. 17.
    Eidenbenz, S., Kumar, V., Zust, S.: Equilibria in topology control games for ad hoc networks. In: Proc. ACM Joint Workshop on Foundations of Mobile Computing (DIALM-POMC) (2003) Google Scholar
  18. 18.
    Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: Proc. 22nd ACM Symposium on Principles of Distributed Computing (PODC), pp. 347–351 (2003) Google Scholar
  19. 19.
    Feldman, M., Chuang, J.: Overcoming free-riding behavior in peer-to-peer systems. ACM Sigecom Exch. 6 (2005) Google Scholar
  20. 20.
    Ganesan, P., Seshadri, M.: On cooperative content distribution and the price of barter. In: Proc. 25th IEEE International Conference on Distributed Computing Systems (ICDCS), pp. 81–90 (2005) Google Scholar
  21. 21.
    Garcia, F.D., Hoepman, J.-H.: Off-line karma: A decentralized currency for peer-to-peer and grid applications. In: Proc. 3rd Applied Cryptography and Network Security (ACNS) Google Scholar
  22. 22.
    Grolimund, D., Meisser, L., Schmid, S., Wattenhofer, R.: Havelaar: A robust and efficient reputation system for active peer-to-peer systems. In: Proc. 1st Workshop on the Economics of Networked Systems (NetEcon), June 2006 Google Scholar
  23. 23.
    Hughes, D., Coulson, G., Walkerdine, J.: Free riding on Gnutella revisited: The bell tolls? IEEE Distrib. Syst. Online 6(6) (2005) Google Scholar
  24. 24.
    Jun, S., Ahamad, M.: Incentives in BitTorrent induce free riding. In: Proc. 3rd ACM SIGCOMM Workshop on Economics of Peer-to-Peer Systems (P2PEcon) (2005) Google Scholar
  25. 25.
    Karger, D.R., Ruhl, M.: Finding nearest neighbors in growth-restricted metrics. In: Proc. 34th ACM Symposium on Theory of Computing (STOC), pp. 741–750 (2002) Google Scholar
  26. 26.
    Locher, T., Moor, P., Schmid, S., Wattenhofer, R.: Free riding in BitTorrent is cheap. In: Proc. 5th Workshop on Hot Topics in Networks (HotNets) (2006) Google Scholar
  27. 27.
    Moscibroda, T., Schmid, S., Wattenhofer, R.: On the topologies formed by selfish peers. In: Proc. 5th International Workshop on Peer-to-Peer Systems (IPTPS) (2006) Google Scholar
  28. 28.
    Moscibroda, T., Schmid, S., Wattenhofer, R.: On the topologies formed by selfish peers. In: Proc. 25th Annual Symposium on Principles of Distributed Computing (PODC) (2006) Google Scholar
  29. 29.
    Odlyzko, A.M.: The case against micropayments. In: Financial Cryptography, pp. 77–83 (2003) Google Scholar
  30. 30.
    Osborne, M., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge (2000) Google Scholar
  31. 31.
    Papadimitriou, C.H.: Algorithms, games, and the Internet. In: Proc. 33rd ACM Symposium on Theory of Computing (STOC), pp. 749–753 (2001) Google Scholar
  32. 32.
    Plaxton, C., Rajaraman, R., Richa, A.W.: Accessing nearby copies of replicated objects in a distributed environment. In: Proc. 9th ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 311–320 (1997) Google Scholar
  33. 33.
    Qiu, D., Srikant, R.: Modeling and performance analysis of BitTorrent-like peer-to-peer systems. In: Proc. ACM SIGCOMM Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications (2004) Google Scholar
  34. 34.
    Roughgarden, T.: Selfish Routing and the Price of Anarchy. MIT Press, Cambridge (2005) Google Scholar
  35. 35.
    Roughgarden, T., Tardos, E.: How bad is selfish routing? J. ACM 49(2) (2002) Google Scholar
  36. 36.
    Rowstron, A., Druschel, P.: Pastry: Scalable, decentralized object location and routing for large-scale peer-to-peer systems. In: Proc. IFIP/ACM Int. Conference on Distributed Systems Platforms (Middleware), pp. 329–350 (2001) Google Scholar
  37. 37.
    Sanghavi, S., Hajek, B.: A new mechanism for the free-rider problem. In: Proc. 3rd ACM SIGCOMM Workshop on Economics of Peer-to-Peer Systems (P2PEcon) (2005) Google Scholar
  38. 38.
    Shneidman, J., Parkes, D.C.: Rationality and self-interest in peer to peer networks. In: Proc. 2nd Int. Workshop on Peer-to-Peer Systems (IPTPS) (2003) Google Scholar
  39. 39.
    Tamilmani, K., Pai, V., Mohr, A.: SWIFT: A system with incentives for trading. In: Proc. 2nd Workshop on Economics of Peer-to-Peer Systems (P2PEcon) (2004) Google Scholar
  40. 40.
    Tovey, C.A.: A simplified NP-complete satisfiability problem. Discrete Appl. Math. 8, 85–89 (1984) MathSciNetMATHCrossRefGoogle Scholar
  41. 41.
    Vishnumurthy, V., Chandrakumar, S., Sirer, E.G.: KARMA: A secure economic framework for P2P resource sharing. In: Proc. 1st Workshop on Economics of Peer-to-Peer Systems (P2PEcon) (2003) Google Scholar
  42. 42.
    Wang, W., Li, B.: Market-driven bandwidth allocation in selfish overlay networks. In: Proc. IEEE Conference on Computer Communications (INFOCOM), pp. 36–46 (2005) Google Scholar
  43. 43.
    Wong, B., Slivkins, A., Sirer, E.G.: Meridian: A lightweight network location service without virtual coordinates. In: Proc. ACM SIGCOMM Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications (2005) Google Scholar
  44. 44.
    Zhao, B.Y., Huang, L., Stribling, J., Rhea, S.C., Joseph, A.D., Kubiatowicz, J.D.: Tapestry: A resilient global-scale overlay for service deployment. IEEE J. Sel. Areas Commun. (2003) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Thomas Moscibroda
    • 1
  • Stefan Schmid
    • 2
  • Roger Wattenhofer
    • 3
  1. 1.Distributed Systems Research GroupMicrosoft ResearchRedmondUSA
  2. 2.Deutsche Telekom Laboratories and Technical University of BerlinBerlinGermany
  3. 3.Computer Engineering and Networks LaboratoryETH ZurichZurichSwitzerland

Personalised recommendations