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Optimal Resource Allocation over Networks via Lottery-Based Mechanisms

  • Soham PhadeEmail author
  • Venkat Anantharam
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 277)

Abstract

We show that, in a resource allocation problem, the ex ante aggregate utility of players with cumulative-prospect-theoretic preferences can be increased over deterministic allocations by implementing lotteries. We formulate an optimization problem, called the system problem, to find the optimal lottery allocation. The system problem exhibits a two-layer structure comprised of a permutation profile and optimal allocations given the permutation profile. For any fixed permutation profile, we provide a market-based mechanism to find the optimal allocations and prove the existence of equilibrium prices. We show that the system problem has a duality gap, in general, and that the primal problem is NP-hard. We then consider a relaxation of the system problem and derive some qualitative features of the optimal lottery structure.

Keywords

Resource allocation Networks Lottery Cumulative prospect theory 

References

  1. 1.
    Altman, E., Wynter, L.: Equilibrium, games, and pricing in transportation and telecommunication networks. Netw. Spatial Econ. 4(1), 7–21 (2004)CrossRefGoogle Scholar
  2. 2.
    Barzel, Y.: A theory of rationing by waiting. J. Law Econ. 17(1), 73–95 (1974)CrossRefGoogle Scholar
  3. 3.
    Boyce, J.R.: Allocation of goods by lottery. Econ. Inquiry 32(3), 457–476 (1994)CrossRefGoogle Scholar
  4. 4.
    Camerer, C.F.: Prospect theory in the wild: evidence from the field. In: Choices, Values, and Frames. pp. 288–300. Contemporary Psychology. No. 47. American Psychology Association, Washington, DC (2001)Google Scholar
  5. 5.
    Chakrabarty, D., Devanur, N., Vazirani, V.V.: New results on rationality and strongly polynomial time solvability in Eisenberg-Gale markets. In: Spirakis, P., Mavronicolas, M., Kontogiannis, S. (eds.) WINE 2006. LNCS, vol. 4286, pp. 239–250. Springer, Heidelberg (2006).  https://doi.org/10.1007/11944874_22CrossRefGoogle Scholar
  6. 6.
    Che, Y.K., Gale, I.: Optimal design of research contests. Am. Econ. Rev. 93(3), 646–671 (2003)CrossRefGoogle Scholar
  7. 7.
    Eckhoff, T.: Lotteries in allocative situations. Inf. (Int. Soc. Sci. Council) 28(1), 5–22 (1989)CrossRefGoogle Scholar
  8. 8.
    Eisenberg, E., Gale, D.: Consensus of subjective probabilities: the pari-mutuel method. Ann. Math. Stat. 30(1), 165–168 (1959)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Falkner, M., Devetsikiotis, M., Lambadaris, I.: An overview of pricing concepts for broadband IP networks. IEEE Commun. Surv. Tutorials 3(2), 2–13 (2000)CrossRefGoogle Scholar
  10. 10.
    Hylland, A., Zeckhauser, R.: The efficient allocation of individuals to positions. J. Polit. Econ. 87(2), 293–314 (1979)CrossRefGoogle Scholar
  11. 11.
    Jain, K., Vazirani, V.V.: Eisenberg-Gale markets: algorithms and game-theoretic properties. Games Econ. Behav. 70(1), 84–106 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47(2), 263–292 (1979)CrossRefGoogle Scholar
  13. 13.
    Kelly, F.: Charging and rate control for elastic traffic. Eur. Trans. Telecommun. 8(1), 33–37 (1997)CrossRefGoogle Scholar
  14. 14.
    Kelly, F.P., Maulloo, A.K., Tan, D.K.: Rate control for communication networks: shadow prices, proportional fairness and stability. J. Oper. Res. Soc. 49(3), 237–252 (1998)CrossRefGoogle Scholar
  15. 15.
    La, R.J., Anantharam, V.: Utility-based rate control in the internet for elastic traffic. IEEE/ACM Trans. Netw. (TON) 10(2), 272–286 (2002)CrossRefGoogle Scholar
  16. 16.
    Lin, X., Shroff, N.B., Srikant, R.: A tutorial on cross-layer optimization in wireless networks. IEEE J. Sel. Areas Commun. 24(8), 1452–1463 (2006)CrossRefGoogle Scholar
  17. 17.
    Mo, J., Walrand, J.: Fair end-to-end window-based congestion control. IEEE/ACM Trans. Netw. 8(5), 556–567 (2000)CrossRefGoogle Scholar
  18. 18.
    Moldovanu, B., Sela, A.: The optimal allocation of prizes in contests. Am. Econ. Rev. 91(3), 542–558 (2001)CrossRefGoogle Scholar
  19. 19.
    Morgan, J.: Financing public goods by means of lotteries. Rev. Econ. Stud. 67(4), 761–784 (2000)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Nagurney, A.: Network Economics: A Variational Inequality Approach, vol. 10. Springer, Heidelberg (2013)zbMATHGoogle Scholar
  21. 21.
    Phade, S.R., Anantharam, V.: Optimal resource allocation over networks via lottery-based mechanisms. arXiv preprint (2018)Google Scholar
  22. 22.
    Prabhakar, B.: Designing large-scale nudge engines. In: ACM SIGMETRICS Performance Evaluation Review, vol. 41, pp. 1–2. ACM (2013)Google Scholar
  23. 23.
    Quiggin, J.: A theory of anticipated utility. J. Econ. Behav. Organ. 3(4), 323–343 (1982)CrossRefGoogle Scholar
  24. 24.
    Quiggin, J.: On the optimal design of lotteries. Economica 58(229), 1–16 (1991)CrossRefGoogle Scholar
  25. 25.
    Stone, P., Political: Why lotteries are just. J. Polit. Philos. 15(3), 276–295 (2007)CrossRefGoogle Scholar
  26. 26.
    Taylor, G.A., Tsui, K.K., Zhu, L.: Lottery or waiting-line auction? J. Public Econ. 87(5–6), 1313–1334 (2003)CrossRefGoogle Scholar
  27. 27.
    Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertainty 5(4), 297–323 (1992)CrossRefGoogle Scholar
  28. 28.
    Von Neumann, J., Morgenstern, O.: Theory of games and economic behavior. Bull. Am. Math. Soc. 51(7), 498–504 (1945)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Wakker, P.P.: Prospect Theory: For Risk and Ambiguity. Cambridge University Press, Cambridge (2010)CrossRefGoogle Scholar
  30. 30.
    Wang, J., Li, L., Low, S.H., Doyle, J.C.: Cross-layer optimization in TCP/IP networks. IEEE/ACM Trans. Netw. (TON) 13(3), 582–595 (2005)CrossRefGoogle Scholar

Copyright information

© ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2019

Authors and Affiliations

  1. 1.University of California at BerkeleyBerkeleyUSA

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