Ilkilic, Rahmi and Kayi, Cagatay (2012): Allocation rules on networks. Published in: Universidad del Rosario  Facultad de Economía SERIE Documentos de Trabajo No. 118

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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 an agent depicts the possibility of a transfer from the source to the agent. Given the supplies 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 consistent and resource monotonic rules in claims problems that satisfy equal treatment of equals. We call these rules fairness principles and we extend fairness principles to allocation rules on networks. We require that for each pair of citizens in the network, the extension is robust with respect to the fairness principle. We call this condition pairwise robustness with respect to the fairness principle. We provide an algorithm and show that each fairness principle has a unique extension which is pairwise robust with respect to the fairness principle. We give applications of the algorithm for three fairness principles: egalitarianism, proportionality and equal sacrifice.
Item Type:  MPRA Paper 

Original Title:  Allocation rules on networks 
Language:  English 
Keywords:  Networks, Claims Problems, Egalitarianism, Proportionality, Equal Sacrifice 
Subjects:  D  Microeconomics > D6  Welfare Economics > D61  Allocative Efficiency; CostBenefit Analysis D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D85  Network Formation and Analysis: Theory Q  Agricultural and Natural Resource Economics; Environmental and Ecological Economics > Q2  Renewable Resources and Conservation > Q20  General 
Item ID:  37305 
Depositing User:  Cagatay Kayi 
Date Deposited:  13. Mar 2012 00:00 
Last Modified:  11. Feb 2013 23:00 
References:  Ambec, S. and L. Ehlers (2008). Sharing a river among satiable agents. Games and Economic Behavior 64, 35–50. Ambec, S. and Y. Sprumont (2002). Sharing a river. Journal of Economic Theory 107, 453–462. Ansink, E. and H. P. Weikard (2009). Contested water rights. European Journal of Political Economy 25, 247–260. Ansink, E. and H. P. Weikard (2011). A strategic model of social and economic networks. Social Choice and Welfare. (forthcoming). Bjorndal, E. and K. Jornsten (2010). Flow sharing and bankruptcy games. International Journal of Game Theory 39, 11–28. Bochet, O., R. Ilkilic, and H. Moulin (2010). Egalitarianism under earmark constraints. mimeo. University of Bern, Bern, Switzerland. Bochet, O., R. Ilkilic, H. Moulin, and J. Sethuraman (2011). Balancing supply and demand under bilateral constraints. Theoretical Economics. (forthcoming). Branzei, R., G. Ferrari, V. Fragnelli, and S. Tijs (2008). A flow approach to bankruptcy problems. AUCO Czech Economic Review 2, 146–153. Brown, J. (1979). The sharing problem. Operations Research 27, 324–340. Hall, N. G. and R. Vohra (1993). Towards equitable distribution via proportional equity constraints. Mathematical Programming 58, 287–294. 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. UNESCOIHE Institute for Water Education. Ilkilic, R. (2007). Network of commons. mimeo. Maastricht University. Maastricht, the Netherlands. Kar, A. and O. Kıbrıs (2008). Allocating multiple estates among agents with singlepeaked preferences. Social Choice and Welfare 31, 641–666. Klaus, B., H. Peters, and T. Storcken (1997). Reallocation of an infinitely divisible good. Economic Theory 10, 305–333. Klaus, B., H. Peters, and T. Storcken (1998). Strategyproof division with singlepeaked preferences and individual endowments. Social Choice and Welfare 15, 297–311. Megiddo, N. (1974). Optimal flows in networks with multiple sources and sinks. Mathematical Programming 7, 97–107. Megiddo, N. (1977). A good algorithm for lexicographically optimal flows in multiterminal networks. Bulletin of the American Mathematical Society 83, 407–409. Moulin, H. (1999). Rationing a commodity along fixed paths. Journal of Economic Theory 84, 41–72. Moulin, H. and J. Sethuraman (2011). The bipartite rationing problem. mimeo. Rice University, Houston, TX, USA. O’Neill, B. (1982). A problem of rights arbitration from the talmud. Mathematical Social Sciences 2, 345–371. Ozdamar, O., E. Ekinci, and B. Kucukyazici (2004). Emergency logistics planning in natural disasters. Annals of Operations Research 129, 217–245. Sprumont, Y. (1991). The division problem with singlepeaked preferences: A characterization of the uniform allocation rule. Econometrica 59, 509–519. Thomson, W. (2003). Axiomatic analysis of bankruptcy and taxation problems: a survey. Mathematical Social Sciences 45, 249–297. Thomson, W. (2006). How to divide when there isnt enough: From the talmud to game theory. mimeo. University of Rochester, Rochester, NY, USA. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/37305 