Mechanism Design with Efficiency and Equality Considerations

  • Zhou Chen
  • Qi Qi
  • Changjun WangEmail author
  • Wenwei Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10660)


In this work, we consider the problem of allocating a set of homogenous resources (goods) among multiple strategic players to balance the efficiency and equality from a game-theoretic perspective. For two very general classes of efficiency measures and equality measures, we develop a general truthful mechanism framework which optimally maximizes the resource holder’s efficiency while guaranteeing certain equality levels. We fully characterize the optimal allocation rule. Based on the characterizations, we show the optimal allocation and corresponding truthful payments can be computed in polynomial time, which means the truthful mechanism is computationally feasible.


  1. 1.
    Atkinson, A.B.: On the measurement of inequality. J. Econ. Theor. 2(3), 244–263 (1970)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bertsimas, D., Farias, V.F., Trichakis, N.: The price of fairness. Oper. Res. 59(1), 17–31 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bertsimas, D., Farias, V.F., Trichakis, N.: On the efficiency-fairness trade-off. Manag. Sci. 58(12), 2234–2250 (2012)CrossRefGoogle Scholar
  4. 4.
    Bodily, S.E.: Police sector design incorporating preferences of interest groups for equality and efficiency. Manag. Sci. 24(12), 1301–1313 (1978)CrossRefzbMATHGoogle Scholar
  5. 5.
    Clarke, E.H.: Multipart pricing of public goods. Public choice 11(1), 17–33 (1971)CrossRefGoogle Scholar
  6. 6.
    Cohon, J.L.: Multiobjective Programming and Planning. Academic Press, Cambridge (1978)zbMATHGoogle Scholar
  7. 7.
    Cole, R., Gkatzelis, V., Goel, G.: Mechanism design for fair division: allocating divisible items without payments. In: Proceedings of the fourteenth ACM conference on Electronic commerce, pp. 251–268. ACM (2013)Google Scholar
  8. 8.
    Corrado, G.: On the measure of concentration with special reference to income and wealth. In: Papers Presented at the Cowles Commission Research Conference on Economics and Statistics (Colorado College Publication, 1936) (1936)Google Scholar
  9. 9.
    Dalton, H.: The measurement of the inequality of incomes. The Econ. J. 30(119), 348–361 (1920)CrossRefGoogle Scholar
  10. 10.
    Drezner, T., Drezner, Z., Guyse, J.: Equitable service by a facility: minimizing the gini coefficient. Comput. Oper. Res. 36(12), 3240–3246 (2009)CrossRefzbMATHGoogle Scholar
  11. 11.
    Golany, B., Tamir, E.: Evaluating efficiency-effectiveness-equality trade-offs: a data envelopment analysis approach. Manag. Sci. 41(7), 1172–1184 (1995)CrossRefzbMATHGoogle Scholar
  12. 12.
    Gopinathan, A., Li, Z.: Strategyproof auctions for balancing social welfare and fairness in secondary spectrum markets. In: INFOCOM, 2011 Proceedings IEEE, pp. 3020–3028. IEEE (2011)Google Scholar
  13. 13.
    Groves, T.: Incentives in teams. Econom. J. Econom. Soc. 41, 617–631 (1973)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Kakwani, N.: On a class of poverty measures. Econom. J. Econom. Soc. 48, 437–446 (1980)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Kozanidis, G.: Solving the linear multiple choice knapsack problem with two objectives: profit and equity. Comput. Optim. Appl. 43(2), 261–294 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Mandell, M.B.: Modelling effectiveness-equity trade-offs in public service delivery systems. Manag. Sci. 37(4), 467–482 (1991)CrossRefGoogle Scholar
  17. 17.
    Maya, A., Nisan, N.: Incentive compatible two player cake cutting. In: Goldberg, P.W. (ed.) WINE 2012. LNCS, vol. 7695, pp. 170–183. Springer, Heidelberg (2012). CrossRefGoogle Scholar
  18. 18.
    Myerson, R.B.: Optimal auction design. Math. Oper. Res. 6(1), 58–73 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Ogryczak, W.: Inequality measures and equitable approaches to location problems. Eur. J. Oper. Res. 122(2), 374–391 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Perugia, A., Moccia, L., Cordeau, J.F., Laporte, G.: Designing a home-to-work bus service in a metropolitan area. Transp. Res. Part B. Methodol. 45(10), 1710–1726 (2011)CrossRefGoogle Scholar
  21. 21.
    Pigou, A.C.: Wealth and welfare. Macmillan and Company Ltd., London (1912)Google Scholar
  22. 22.
    Sauer, P., Zagler, M.: Economic growth and the quantity and distribution of education: a survey. J. Econ. Surv. 26(5), 933–951 (2012)CrossRefGoogle Scholar
  23. 23.
    Sen, A.: On Economic Inequality. Clarendon Paperbacks, Clarendon Press (1973).
  24. 24.
    Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. J. Finan. 16(1), 8–37 (1961)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Weymark, J.A.: Generalized gini inequality indices. Math. Soc. Sci. 1(4), 409–430 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Zivan, R., Dudik, M., Okamoto, S., Sycara, K.: Reducing untruthful manipulation in envy-free pareto optimal resource allocation. In: 2010 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology (WI-IAT), vol. 2, pp. 391–398. IEEE (2010)Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Hong Kong University of Science and TechnologyClear Water BayHong Kong
  2. 2.Beijing University of TechnologyBeijingChina

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