Allocation rules on networks

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).

Myopic reallocation of extraction improves collective outcomes in networked common-pool resource games

“…We believe that the findings presented here might provide a more fundamental basis upon which to build these more elaborate networked CPR models, which incorporate additional social processes which interact with agents' myopic self-interest to facilitate or hinder effective CPR self-regulation by reallocation. Finally, we expect that it will be fruitful to explore potential links between the present work, which is rooted in a more abstract, evolutionary perspective, and the wider body of ongoing applied research that applies the tools of rational queueing theory 33,34 , dynamic pricing [35][36][37] , and social choice theory 38 to address issues of resource allocation in networked systems [39][40][41][42] . Although the CPR literature may seem to suggest that regulation by a centralized decision-maker is likely doomed to failure, a study of the mechanisms underlying CPR self-regulation may help to inform research undertaken from an optimal control perspective, with the aim of identifying potential targeted interventions that respect and leverage a community's innate capacity for bottom-up self-regulation rather than disrupt it.…”

A new framework for resolving conflicts over transboundary rivers using bankruptcy methods

“…While temporal resource variability has not been considered in previous bankruptcy studies, few studies have tried to address the spatial variability of resource in bankruptcy problems. Ilkılıç and Kayı (2012) formulated a network (graph) model for bankruptcy allocation with respect to the possible geographical and infrastructural constraints in distributing the resource among beneficiaries. While their method satisfies the fairness principle, i.e., "equal treatment of the equals", it considers "no restrictions on the possible networks between sources and agents" (Ilkılıç and Kayı, 2012).…”

“…Ilkılıç and Kayı (2012) formulated a network (graph) model for bankruptcy allocation with respect to the possible geographical and infrastructural constraints in distributing the resource among beneficiaries. While their method satisfies the fairness principle, i.e., "equal treatment of the equals", it considers "no restrictions on the possible networks between sources and agents" (Ilkılıç and Kayı, 2012). Therefore, their model is not generally applicable to river sharing problems in which the physical characteristics of the resource (river) system impose restrictions on networks between sources (river sections) and agents (riparian parties).…”

“…While transboundary water allocation motivates this work, the proposed method is applicable to other bankruptcy problems with temporal and spatial resource availability constraints. Suggested examples of such problems by Ilkılıç and Kayı (2012) include aid relief during and after disasters, utility (gas, electricity, water) distribution in supply shocks, and common property fisheries.…”