Social Choice and Welfare

, Volume 43, Issue 4, pp 877–892 | Cite as

Allocation rules on networks

Article

Abstract

When allocating a resource, geographical and infrastructural constraints have to be taken into account. We study the problem of distributing a resource through a network from sources endowed with the resource to citizens with claims. A link between a source and a citizen depicts the possibility of a transfer from the source to the citizen. Given the endowments at each source, the claims of citizens, and the network, the question is how to allocate the available resources among the citizens. We consider a simple allocation problem that is free of network constraints, where the total amount can be freely distributed. The simple allocation problem is a claims problem where the total amount of claims is greater than what is available. We focus on resource monotonic and anonymous bilateral principles satisfying a regularity condition and extend these principles to allocation rules on networks. We require the extension to preserve the essence of the bilateral principle for each pair of citizens in the network. We call this condition pairwise robustness with respect to the bilateral principle. We provide an algorithm and show that each bilateral principle has a unique extension which is pairwise robust (Theorem 1). Next, we consider a Rawlsian criteria of distributive justice and show that there is a unique “Rawls fair” rule that equals the extension given by the algorithm (Theorem 2). Pairwise robustness and Rawlsian fairness are two sides of the same coin, the former being a pairwise and the latter a global requirement on the allocation given by a rule. We also show as a corollary that any parametric principle can be extended to an allocation rule (Corollary 1). Finally, we give applications of the algorithm for the egalitarian, the proportional, and the contested garment bilateral principles (Example 1).

References

  1. Ambec S, Ehlers L (2008) Sharing a river among satiable agents. Games Econ Behav 64:35–50CrossRefGoogle Scholar
  2. Ambec S, Sprumont Y (2002) Sharing a river. J Econ Theory 107:453–462CrossRefGoogle Scholar
  3. Ansink E, Weikard HP (2009) Contested water rights. Eur J Political Econ 25:247–260CrossRefGoogle Scholar
  4. Ansink E, Weikard HP (2012) Sequential sharing rules for river sharing problems. Soc Choice Welf 38:187–210CrossRefGoogle Scholar
  5. Aumann RJ, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the Talmud. J Econ Theory 36:195–213CrossRefGoogle Scholar
  6. Bjørndal E, Jörnsten K (2010) Flow sharing and bankruptcy games. Int J Game Theory 39:11–28CrossRefGoogle Scholar
  7. Bochet O, İlkılıç R, Moulin H (2013) Egalitarianism under earmark constraints. J Econ Theory 148:535–562CrossRefGoogle Scholar
  8. Bochet O, İlkılıç R, Moulin H, Sethuraman J (2012) Balancing supply and demand under bilateral constraints. Theor Econ 7:395–423CrossRefGoogle Scholar
  9. Branzei R, Ferrari G, Fragnelli V, Tijs S (2008) A flow approach to bankruptcy problems. AUCO Czech Econ Rev 2:146–153Google Scholar
  10. Brown J (1979) The sharing problem. Oper Res 27:324–340CrossRefGoogle Scholar
  11. Chun Y (1999) Equivalance of axioms for bankruptcy problems. Int J Game Theory 28:511–520CrossRefGoogle Scholar
  12. Dagan N, Volij O (1997) Bilateral comparisons and consistent fair division rules in the context of bankruptcy problems. Int J Game Theory 26:11–25CrossRefGoogle Scholar
  13. Hall NG, Vohra R (1993) Towards equitable distribution via proportional equity constraints. Math Program 58:287–294CrossRefGoogle Scholar
  14. Hoekstra A (2006) The global dimension of water governance: nine reasons for global arrangements in order to cope with local problems. Value of Water Research Report Series 20. UNESCO-IHE Institute for Water EducationGoogle Scholar
  15. Hokari T, Thomson W (2008) On the properties of division rules lifted by bilateral consistency. J Math Econ 44:211–231CrossRefGoogle Scholar
  16. İlkılıç R (2011) Networks of common property resources. Econ Theory 47:105–134CrossRefGoogle Scholar
  17. Kar A, Kıbrıs O (2008) Allocating multiple estates among agents with single-peaked preferences. Soc Choice Welf 31:641–666CrossRefGoogle Scholar
  18. Kıbrıs O, Küçükşenel S (2009) Uniform trade rules for uncleared markets. Soc Choice Welf 32:101–121CrossRefGoogle Scholar
  19. Klaus B, Peters H, Storcken T (1997) Reallocation of an infinitely divisible good. Econ Theory 10:305–333CrossRefGoogle Scholar
  20. Klaus B, Peters H, Storcken T (1998) Strategy-proof division with single-peaked preferences and individual endowments. Soc Choice Welf 15:297–311CrossRefGoogle Scholar
  21. Megiddo N (1974) Optimal flows in networks with multiple sources and sinks. Math Program 7:97–107CrossRefGoogle Scholar
  22. Megiddo N (1977) A good algorithm for lexicographically optimal flows in multi-terminal networks. Bull Am Math Soc 83:407–409CrossRefGoogle Scholar
  23. Moulin H (1999) Rationing a commodity along fixed paths. J of Econ Theory 84:41–72CrossRefGoogle Scholar
  24. Moulin H, Sethuraman J (2013) The bipartite rationing problem. Oper Res 61:1087–1100CrossRefGoogle Scholar
  25. O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2:345–371CrossRefGoogle Scholar
  26. Özdamar O, Ekinci E, Küçükyazıcı B (2004) Emergency logistics planning in natural disasters. Ann Oper Res 129:217–245CrossRefGoogle Scholar
  27. Rawls J (1971) A theory of justice. Harvard University Press, CambridgeGoogle Scholar
  28. Sprumont Y (1991) The division problem with single-peaked preferences: a characterization of the uniform allocation rule. Econometrica 59:509–519CrossRefGoogle Scholar
  29. Szwagrzak KF (2011) The replacement principle in networked economies with single-peaked preferences. mimeo. University of Southern Denmark, OdenseGoogle Scholar
  30. Thomson W (2003) Axiomatic analysis of bankruptcy and taxation problems: a survey. Math Soc Sci 45:249–297CrossRefGoogle Scholar
  31. Thomson W (2006) How to divide when there isnt enough: from the Talmud to game theory. mimeo. University of Rochester, RochesterGoogle Scholar
  32. Young HP (1987) On dividing an amount according to individual claims or liabilities. Math Oper Res 12:398–414CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of EconomicsBilkent UniversityAnkaraTurkey
  2. 2.Facultad de EconomíaUniversidad del RosarioBogotáColombia

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