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.

We analyse agreements on river water allocation between riparian countries. Besides being efficient, water allocation agreements need to be stable in order to be effective in increasing the efficiency of water use. In this paper we assess the stability of water allocation agreements using a game theoretic model. We consider the effects of climate change and the choice of a sharing rule on stability. Our results show that a decrease in mean river flow decreases the stability of an agreement, while an increased variance can have a positive or a negative effect on stability. An agreement where the downstream country is allocated a fixed amount of water has the lowest stability compared to other sharing rules. These results hold for both constant and flexible non-water transfers.

We analyse the threats of global environmental change, as they relate to food security. First, we review three discourses: (i) ‘sustainable intensification’, or the increase of food supplies without compromising food producing inputs, such as soils and water; (ii) the ‘nexus’ that seeks to understand links across food, energy, environment and water systems; and (iii) ‘resilience thinking’ that focuses on how to ensure the critical capacities of food, energy and water systems are maintained in the presence of uncertainties and threats. Second, we build on these discourses to present the causal, risks and options assessment for decision‐making process to improve decision‐making in the presence of risks. The process provides a structured, but flexible, approach that moves from problem diagnosis to better risk‐based decision‐making and outcomes by responding to causal risks within and across food, energy, environment and water systems.