Sequential sharing rules for river sharing problems

Abstract

We analyse the redistribution of a resource amongst agents who have claims to the resource and who are ordered linearly. A well known example of this particular situation is the river sharing problem. We exploit the linear order of agents to transform the river sharing problem to a sequence of two-agent river sharing problems. These reduced problems are mathematically equivalent to bankruptcy problems and can therefore be solved using any bankruptcy rule. Our proposed class of solutions, that we call sequential sharing rules, solves the river sharing problem. Our approach extends the bankruptcy literature to settings with a sequential structure of both the agents and the resource to be shared. In the paper, we first characterise the class of sequential sharing rules. Subsequently, we apply sequential sharing rules based on four classical bankruptcy rules, assess their properties, provide two characterisations of one specific rule, and compare sequential sharing rules with three alternative solutions to the river sharing problem.

Weighted Bankruptcy Rules and Transboundary Water Resources Allocation

“…A comparative analysis of four classical solutions (PRO, CEA, CEL, and TAL) from an axiomatic viewpoint was provided in Herrero and Villar (2001). Ansink and Weikard (2012) present a class of sequential sharing rules (SSRs). Each rule in this class is based on a given bankruptcy rule, such as PRO, CEA or CEL.…”

“…Ansink and Marchiori (2010), Ansink and Weikard (2012), and Mianabadi et al (2014a) used it in water resources management. Zarezadeh et al (2012) applied four bankruptcy rules including PRO, AP, CEL and CEA to suggest the most acceptable allocation scheme for different scenarios of future development and climate for Qezelozan-Sefidrood River Basin in Iran.…”

“…In river sharing problems this may be the case. One significant limitation of some of previously mentioned methods, such as Ambec's methods (Ambec and Sprumont 2002;Ambec et al 2013), SSRs (Ansink and Weikard 2012), or Ambec and Ehlers's allocation method (Ambec and Ehlers 2008) is that agents should be ordered linearly along water resource. Thus, they are not applicable to reallocate complex multitributary transboundray river systems and other natural resources including lakes, groundwater aquifers, and shared sea resources.…”

“…The objective of a bankruptcy rule is to specify the allocation of each agent which is denoted by x i =ψ i (E,c,a)≥0 such that (a) ∑ i =1 n x i =∑ i=1 n a i =E for all i∈N, (b) 0≤x i ≤c i , and (C) x i ≤E,∀i∈N. Requirement (a), the sum of all allocations is equal to the available asset, imposes 'efficiency' (Ansink and Weikard 2012). Requirement (b) says that the allocation x i that each agent obtains is non-negative and not larger than his claim c i (Mianabadi et al 2014a).…”

Transboundary Externalities and Property Rights: An International River Pollution Model

“…Dinar (1995, 2001), Ambec and Sprumont (2002), Ambec and Ehlers (2008), Khmelnitskaya (2010), Wang (2011), van den all use game-theoretic models to investigate the distribution of water among countries sharing an international river. In Ansink and Weikard (2011) and van den Brink, Estévez-Fernández, van der Laan and Moes (2011) a closely related axiomatic approach is followed.…”