Economic Theory

, Volume 36, Issue 3, pp 379–405 | Cite as

The price of anarchy of serial, average and incremental cost sharing

Research Article

Abstract

We compute the price of anarchy (PoA) of three familiar demand games, i.e., the smallest ratio of the equilibrium to efficient surplus, over all convex preferences quasi-linear in money. For any convex cost, the PoA is at least \(\frac{1}{n}\) in the average and serial games, where n is the number of users. It is zero in the incremental game for piecewise linear cost functions. With quadratic costs, the PoA of the serial game is \(\theta (\frac{1}{\log n})\) , and \(\theta (\frac{1}{n})\) for the average and incremental games. This generalizes if the marginal cost is convex or concave, and its elasticity is bounded.

Keywords

Price of anarchy Cost sharing Average cost Serial cost Incremental cost 

JEL Classification Numbers

C60 C72 D60 

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References

  1. Anshelevich, E., Dasgupta, A., Tardos, E., Wexler, T.: Near-optimal network design with selfish agents. In: Proceedings of the 35th Annual ACM Symposium on the Theory of Computing (2004)Google Scholar
  2. Billera L., Heath D.C. (1982) Allocation of shared costs: a set of axioms yielding a unique procedure. Maths Oper Res 7, 32–39CrossRefGoogle Scholar
  3. Binmore, K.: Fun and Games. New York: Heath and Cy (1992)Google Scholar
  4. Chen, Y., Zhang, J.: Design of price mechanisms for network resource allocation via price of anarchy, mimeo. New York University (2005)Google Scholar
  5. Cres H., Moulin H. (2003) Commons with increasing marginal cost: random priority versus average cost. Int Econ Rev 44(3): 1097–1115CrossRefGoogle Scholar
  6. Dasgupta P., Heal G. (1979) Economic Theory and Exhaustible Resources. Cambridge, Cambridge University PressGoogle Scholar
  7. Demers A., Keshaw S., Shenker S. (1990) Analysis and simulation of a fair queuing algorithm. Internetwork Res Exp 1, 3–26Google Scholar
  8. Friedman, E.: A generic analysis of selfish routing. In: Proceedings of the 43rd IEEE Conference on Decision and Control (2004a)Google Scholar
  9. Friedman, E.: Asynchronous learning in decentralized environments: A game theoretic approach. In: Tumer, K., Wolpert, D. (eds.) Collectives and the Design of Complex Systems. Heidelberg: Springer (2004b)Google Scholar
  10. Johari R., Tsitsiklis J. (2004) Efficiency loss in a network resource allocation game. Maths Oper Res 29(3): 407–435CrossRefGoogle Scholar
  11. Johari, R., Tsitsiklis, J.: A scalable network resource allocation mechanism. IEEE Selected Areas Commun (2006) (in press)Google Scholar
  12. Johari R., Mannor S., Tsitsiklis J. (2005). Efficiency loss in a network resource allocation game: the case of elastic supply. IEEE Trans Automatic Control 50(11): 1712–1724CrossRefGoogle Scholar
  13. Juarez, R.: The worst absolute surplus loss in the problem of the commons: random priority versus average cost. Econ Theory (2007) (in press)Google Scholar
  14. Koutsoupias, E., Papadimitriou, C.: Worst case equilibria. In: Proceedings of the 16th Symposium on Theoretical Aspects of Computer Science, pp. 404–413 (1999)Google Scholar
  15. Leroux J. (2007) Cooperative production with diminishing marginal returns: Interpreting fixed-path methods. Soc Choice Welfare 29(1): 35–54 (in press)CrossRefGoogle Scholar
  16. Monderer D., Shapley L. (1996a). Fictitious play property for games with identical interests. J Econ Theory 68, 258–265CrossRefGoogle Scholar
  17. Monderer D., Shapley L. (1996b). Potential games. Games Econ Behav 14, 124–143CrossRefGoogle Scholar
  18. Moulin, H.: The price of anarchy of serial cost sharing and other methods. http://www.ruf.rice.edu/~econ/faculty/Moulin.htm (2005)
  19. Moulin, H.: Efficient cost sharing with a cheap residual claimant. http://www.ruf.rice.edu/~econ/faculty/Moulin.htm (2006)
  20. Moulin H., Shenker S. (1992). Serial cost sharing. Econometrica 60, 1009–1037CrossRefGoogle Scholar
  21. Moulin H., Shenker S. (1994) Average cost pricing versus serial cost sharing: an axiomatic comparison. J Econ Theory 64, 178–201CrossRefGoogle Scholar
  22. Moulin H., Shenker S. (2001) Strategy-proof sharing of submodular costs: budget balance versus efficiency. Econ Theory 18(3): 511–533CrossRefGoogle Scholar
  23. Moulin H., Sprumont Y. (2005). On demand responsiveness in additive cost sharing. J Econ Theory 125, 1–35CrossRefGoogle Scholar
  24. Moulin H., Watts A. (1997). Two versions of the tragedy of the commons. Econ Design 2, 399–421CrossRefGoogle Scholar
  25. Roughgarden, T.: The price of anarchy is independent of the network topology. STOC (2002a)Google Scholar
  26. Roughgarden T., Tardos E. (2002b). How bad is selfish routing?. J ACM 49(2): 236–259CrossRefGoogle Scholar
  27. Samet D., Tauman Y. (1982) The determination of marginal cost prices under a set of axioms. Econometrica 50, 895–909CrossRefGoogle Scholar
  28. Sandholm W. (2001). Potential games with continuous player sets. J Econ Theory 97, 81–108CrossRefGoogle Scholar
  29. Sanghavi, S., Hajek, B.: Optimal allocation of a divisible good to strategic buyers. In: Proceedings of the 43d IEEE Conference on Decision and Control (2004)Google Scholar
  30. Sen A.K. (1966) Labour allocation in a cooperative enterprise. Rev Econ Stud 33, 361–371CrossRefGoogle Scholar
  31. Shenker S. (1995) Making greed work in networks: a game-theoretical analysis of gateway service disciplines. IEEE/ACM Trans on Network 3(6): 819–831 (circulated 1989)CrossRefGoogle Scholar
  32. Sorenson J., Tschirhart J., Whinston A. (1978) A theory of pricing under decreasing costs. Am Econ Rev 68, 614–624Google Scholar
  33. Sprumont Y. (1998) Ordinal cost sharing. J Econ Theory 81, 126–162CrossRefGoogle Scholar
  34. Suh, S.C.: Two serial mechanisms in a surplus-sharing problem, mimeo. University of Windsor (1997)Google Scholar
  35. Watts A. (1996) On the uniqueness of equilibrium in Cournot oligopoly and other games. Games Econ Behav 13, 269–285CrossRefGoogle Scholar
  36. Weizman M. (1974) Free access versus private ownership as alternative systems for managing common property. J Econ Theory 8, 225–234CrossRefGoogle Scholar
  37. Yang, S., Hajek, B.: Revenue and stability of a mechanism for efficient allocation of a divisible good, mimeo. Urbana Champaign: University of Illinois (2005)Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of EconomicsRice UniversityHoustonUSA

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