Advertisement

Group Envy Freeness and Group Pareto Efficiency in Fair Division with Indivisible Items

  • Martin AleksandrovEmail author
  • Toby WalshEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11117)

Abstract

We study the fair division of items to agents supposing that agents can form groups. We thus give natural generalizations of popular concepts such as envy-freeness and Pareto efficiency to groups of fixed sizes. Group envy-freeness requires that no group envies another group. Group Pareto efficiency requires that no group can be made better off without another group be made worse off. We study these new group properties from an axiomatic viewpoint. We thus propose new fairness taxonomies that generalize existing taxonomies. We further study near versions of these group properties as allocations for some of them may not exist. We finally give three prices of group fairness between group properties for three common social welfares (i.e. utilitarian, egalitarian and Nash).

Keywords

Multi-agent systems Social choice Group Fair Division 

References

  1. 1.
    Aleksandrov, M., Aziz, H., Gaspers, S., Walsh, T.: Online fair division: analysing a food bank problem. In: Proceedings of the Twenty-Fourth IJCAI 2015, Buenos Aires, Argentina, 25–31 July 2015, pp. 2540–2546 (2015)Google Scholar
  2. 2.
    Aleksandrov, M., Walsh, T.: Most competitive mechanisms in online fair division. In: Kern-Isberner, G., Fürnkranz, J., Thimm, M. (eds.) KI 2017. LNCS (LNAI), vol. 10505, pp. 44–57. Springer, Cham (2017)CrossRefGoogle Scholar
  3. 3.
    Aleksandrov, M., Walsh, T.: Pure Nash equilibria in online fair division. In: Sierra, C. (ed.) Proceedings of the Twenty-Sixth IJCAI 2017, Melbourne, Australia, pp. 42–48 (2017)Google Scholar
  4. 4.
    Aziz, H., Bouveret, S., Caragiannis, I., Giagkousi, I., Lang, J.: Knowledge, fairness, and social constraints. In: Proceedings of the Thirty-Second AAAI 2018, New Orleans, Louisiana, USA, 2–7 February 2018. AAAI Press (2018)Google Scholar
  5. 5.
    Aziz, H., Mackenzie, S., Xia, L., Ye, C.: Ex post efficiency of random assignments. In: Proceedings of the 2015 International AAMAS Conference, Istanbul, Turkey, 4–8 May 2015, pp. 1639–1640. IFAAMAS (2015)Google Scholar
  6. 6.
    Aziz, H., Rauchecker, G., Schryen, G., Walsh, T.: Algorithms for max-min share fair allocation of indivisible chores. In: Proceedings of the Thirty-First AAAI 2017, San Francisco, California, USA, 4–9 February 2017, pp. 335–341. AAAI Press (2017)Google Scholar
  7. 7.
    Bertsimas, D., Farias, V.F., Trichakis, N.: The price of fairness. Operations Research 59(1), 17–31 (2011)Google Scholar
  8. 8.
    Bliem, B., Bredereck, R., Niedermeier, R.: Complexity of efficient and envy-free resource allocation: few agents, resources, or utility levels. In: Proceedings of the Twenty-Fifth IJCAI 2016, New York, NY, USA, 9–15 July 2016, pp. 102–108 (2016)Google Scholar
  9. 9.
    Bogomolnaia, A., Moulin, H.: A new solution to the random assignment problem. Journal of Economic Theory 100(2), 295–328 (2001)Google Scholar
  10. 10.
    Bogomolnaia, A., Moulin, H., Sandomirskiy, F., Yanovskaya, E.: Dividing goods and bads under additive utilities. CoRR abs/1610.03745 (2016)Google Scholar
  11. 11.
    Borsuk, K.: Drei Stze über die n-dimensionale euklidische Sphäre. Fundamenta Mathematicae 20(1), 177–190 (1933)Google Scholar
  12. 12.
    Bouveret, S., Cechlárová, K., Elkind, E., Igarashi, A., Peters, D.: Fair division of a graph. In: Proceedings of the Twenty-Sixth IJCAI 2017, 19–25 August 2017, pp. 135–141 (2017)Google Scholar
  13. 13.
    Bouveret, S., Lang, J.: Efficiency and envy-freeness in fair division of indivisible goods: logical representation and complexity. Journal of AI Research (JAIR) 32, 525–564 (2008)Google Scholar
  14. 14.
    Brams, S.J., Fishburn, P.C.: Fair division of indivisible items between two people with identical preferences: envy-freeness, pareto-optimality, and equity. Social Choice and Welfare 17(2), 247–267 (2000)Google Scholar
  15. 15.
    Brams, S.J., King, D.L.: Efficient fair division: help the worst off or avoid envy? Rationality and Society 17(4), 387–421 (2005)Google Scholar
  16. 16.
    Brams, S.J., Taylor, A.D.: Fair Division - From Cake-cutting to Dispute Resolution. Cambridge University Press, Cambridge (1996)CrossRefGoogle Scholar
  17. 17.
    de Clippel, G.: Equity, envy and efficiency under asymmetric information. Economics Letters 99(2), 265–267 (2008)Google Scholar
  18. 18.
    Davidson, P., Evans, R.: Poverty in Australia. ACOSS (2014)Google Scholar
  19. 19.
    Debreu, G.: Preference functions on measure spaces of economic agents. Econometrica 35(1), 111–122 (1967)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Dorsch, P., Phillips, J., Crowe, C.: Poverty in Australia. ACOSS (2016)Google Scholar
  21. 21.
    Dubins, L.E., Spanier, E.H.: How to cut a cake fairly. The American Mathematical Monthly 68(1), 1–17 (1961)Google Scholar
  22. 22.
    Hill, T.P.: Determining a fair border. The American Mathematical Monthly 90(7), 438–442 (1983)Google Scholar
  23. 23.
    Husseinov, F.: A theory of a heterogeneous divisible commodity exchange economy. Journal of Mathematical Economics 47(1), 54–59 (2011)Google Scholar
  24. 24.
    Kaleta, M.: Price of fairness on networked auctions. Journal of Applied Mathematics 2014, 1–7 (2014)Google Scholar
  25. 25.
    de Keijzer, B., Bouveret, S., Klos, T., Zhang, Y.: On the complexity of efficiency and envy-freeness in fair division of indivisible goods with additive preferences. In: Rossi, F., Tsoukias, A. (eds.) ADT 2009. LNCS (LNAI), vol. 5783, pp. 98–110. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  26. 26.
    Kokoye, S.E.H., Tovignan, S.D., Yabi, J.A., Yegbemey, R.N.: Econometric modeling of farm household land allocation in the municipality of Banikoara in northern Benin. Land Use Policy 34, 72–79 (2013)CrossRefGoogle Scholar
  27. 27.
    Lahaie, S., Parkes, D.C.: Fair package assignment. In: Auctions, Market Mechanisms and Their Applications, First International ICST Conference, AMMA 2009, Boston, MA, USA, 8–9 May 2009, Revised Selected Papers, p. 92 (2009)Google Scholar
  28. 28.
    Lumet, C., Bouveret, S., Lemaître, M.: Fair division of indivisible goods under risk. In: ECAI. Frontiers in AI and Applications, vol. 242, pp. 564–569. IOS Press (2012)Google Scholar
  29. 29.
    Manurangsi, P., Suksompong, W.: Computing an approximately optimal agreeable set of items. In: Proceedings of the Twenty-Sixth IJCAI 2017, Melbourne, Australia, 19–25 August 2017, pp. 338–344 (2017)Google Scholar
  30. 30.
    Nicosia, G., Pacifici, A., Pferschy, U.: Price of fairness for allocating a bounded resource. European Journal of Operational Research 257(3), 933–943 (2017)Google Scholar
  31. 31.
    Parkes, D.C., Procaccia, A.D., Shah, N.: Beyond dominant resource fairness: extensions, limitations, and indivisibilities. ACM Transactions 3(1), 1–22 (2015)Google Scholar
  32. 32.
    Schmeidler, D., Vind, K.: Fair net trades. Econometrica 40(4), 637–642 (1972)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Segal-Halevi, E., Nitzan, S.: Fair cake-cutting among groups. CoRR abs/1510.03903 (2015)Google Scholar
  34. 34.
    Segal-Halevi, E., Suksompong, W.: Democratic fair division of indivisible goods. In: Proceedings of the Twenty-Seventh IJCAI-ECAI 2018, Stockholm, Sweden, 13–19 July 2018 (2018)Google Scholar
  35. 35.
    Smet, P.: Nurse rostering: models and algorithms for theory, practice and integration with other problems. 4OR 14(3), 327–328 (2016)Google Scholar
  36. 36.
    Steinhaus, H.: The problem of fair division. Econometrica 16(1), 101–104 (1948)Google Scholar
  37. 37.
    Stone, A.H., Tukey, J.W.: Generalized sandwich theorems. Duke Mathematical Journal 9(2), 356–359 (1942)Google Scholar
  38. 38.
    Suksompong, W.: Assigning a small agreeable set of indivisible items to multiple players. In: Proceedings of the Twenty-Fifth IJCAI 2016, New York, NY, USA, 9–15 July 2016, pp. 489–495. IJCAI/AAAI Press (2016)Google Scholar
  39. 39.
    Suksompong, W.: Approximate maximin shares for groups of agents. Mathematical Social Sciences 92, 40–47 (2018)Google Scholar
  40. 40.
    Todo, T., Li, R., Hu, X., Mouri, T., Iwasaki, A., Yokoo, M.: Generalizing envy-freeness toward group of agents. In: Proceedings of the Twenty-Second IJCAI 2011, Barcelona, Catalonia, Spain, 16–22 July 2011, pp. 386–392 (2011)Google Scholar
  41. 41.
    Varian, H.R.: Equity, envy, and efficiency. Journal of Economic Theory 9(1), 63–91 (1974)Google Scholar
  42. 42.
    Vind, K.: Edgeworth-allocations in an exchange economy with many traders. International Economic Review 5(2), 165–177 (1964)Google Scholar
  43. 43.
    Weller, D.: Fair division of a measurable space. Journal of Mathematical Economics 14(1), 5–17 (1985)Google Scholar
  44. 44.
    Yokoo, M.: Characterization of strategy/false-name proof combinatorial auction protocols: price-oriented, rationing-free protocol. In: Proceedings of the Eighteenth IJCAI 2003, Acapulco, Mexico, 9–15 August 2003, pp. 733–742 (2003)Google Scholar
  45. 45.
    Zhou, L.: Strictly fair allocations in large exchange economies. Journal of Economic Theory 57(1), 158–175 (1992)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Technical University of BerlinBerlinGermany

Personalised recommendations