The Efficiency and Fairness of a Fixed Budget Resource Allocation Game

  • Li Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3580)


We study the resource allocation game in which price anticipating players compete for multiple divisible resources. In the scheme, each player submits a bid to a resource and receives a share of the resource according to the proportion of his bid to the total bids. Unlike the previous study (e.g.[5]), we consider the case when the players have budget constraints, i.e. each player’s total bids is fixed. We show that there always exists a Nash equilibrium when the players’ utility functions are strongly competitive. We study the efficiency and fairness at the Nash equilibrium. We show the tight efficiency bound of \(\theta(1/\sqrt{m})\) for the m player balanced game. For the special cases when there is only one resource or when there are two players with linear utility functions, the efficiency is 3/4. We extend the classical notion of envy-freeness to measure fairness. We show that despite a possibly large utility gap, any Nash equilibrium is 0.828-approximately envy-free in this game.


Utility Function Nash Equilibrium Budget Constraint Allocation Scheme Congestion Game 
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  1. 1.
    Brams, S.J., Taylor, A.D.: Fair Division: From Cake-cutting to Dispute Resolution. Cambridge University Press, Cambridge (1996)zbMATHGoogle Scholar
  2. 2.
    Chun, B.N., Culler, D.E.: Market-based proportional resource sharing for clusters. Technical Report CSD-1092, University of California at Berkeley, Computer Science Division (January 2000)Google Scholar
  3. 3.
    Feldman, M., Lai, K., Zhang, L.: A price-anticipating resource allocation mechanism for distributed shared clusters. In: Proceedings of ACM Conference on Electronic Commerce (2005)Google Scholar
  4. 4.
    Ferguson, D., Yemimi, Y., Nikolaou, C.: Microeconomic algorithms for load balancing in distributed computer systems. In: International Conference on Distributed Computer Systems, pp. 491–499 (1988)Google Scholar
  5. 5.
    Johari, R., Tsitsiklis, J.N.: Efficiency loss in a network resource allocation game. Mathematics of Operations Research (2004)Google Scholar
  6. 6.
    Kelly, F.P.: Charging and rate control for elastic traffic. European Transactions on Telecommunications 8, 33–37 (1997)CrossRefGoogle Scholar
  7. 7.
    Kelly, F.P., Maulloo, A.: Rate control in communication networks: Shadow prices, proportional fairness and stability. Operational Res. Soc. 49, 237–252 (1998)zbMATHGoogle Scholar
  8. 8.
    Korilis, Y., Lazar, A.: Why is flow control hard: optimality, fairness, partial and delayed information. In: Proceedings of 2nd ORSA Telecommunications Conference (1992)Google Scholar
  9. 9.
    Lai, K., Rasmusson, L., Sorkin, S., Zhang, L., Huberman, B.A.: Tycoon: a distributed market-based resource allocation system. (2004) (manuscript),
  10. 10.
    Maheswaran, R.T., Basar, T.: Nash equilibrium and decentralized negotiation in acutioning divisible resources. Group Decision and Negotiation 12, 361–395 (2003)CrossRefGoogle Scholar
  11. 11.
    Milchtaich, I.: Congestion games with player-specific payoff functions. Games and Economic Behavior 13, 111–124 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Monderer, D., Sharpley, L.S.: Potential games. Games and Economic Behavior 14, 124–143 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Papadimitriou, C.: Algorithms, games, and the Internet. In: Proceedings of 33rd Annual ACM Symposium on Theory of Computing, pp. 749–753 (2001)Google Scholar
  14. 14.
    Regev, O., Nisan, N.: The POPCORN market – an online market for computational resources. In: Proceedings of 1st International Conference on Information and Computation Economies, pp. 148–157 (1998)Google Scholar
  15. 15.
    Rosen, J.B.: Existence and uniqueness of equilibrium points for concave N-person games. Econometrica 33(3), 520–534 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Roughgarden, T., Tardos, E.: How bad is selfish routing? Jounral of the ACM 49(2), 236–259 (2002)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Varian, H.R.: Equity, envy, and efficiency. Journal of Economic Theory 9, 63–91 (1974)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Waldspurger, C.A., Hogg, T., Huberman, B.A., Kephart, J.O., Stornetta, W.S.: Spawn: A distributed computational economy. Software Engineering 18(2), 103–117 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Li Zhang
    • 1
  1. 1.Hewlett-Packard LabsPalo AltoUSA

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