Introduction

Water consumption reduction often arises as a sustainable adaptation pathway under water scarcity conditions. Often, administrative units subsidize water users in order to promote water consumption reduction, either directly or indirectly through water pricing policies. However, horizontal measures might fail to address the complexity of the problem, promoting suboptimal or unfair strategies. We present a methodological framework that can be used to fairly subsidize water consumption reduction in water distribution networks.

Methodology

First, we use graph theory in order to represent water distribution networks. Typically, Nodes represent water consumption junctions and Edges represent water pipes. Then, we model the networks using python package “epanettools”, which has been developed in order to perform EPANET simulations in Python. We consider the Nodes as Players (or groups of Players) under a game theoretical framework. We assume that every player reduces their consumption, resulting in an overall consumption reduction for the water distribution system. This reduction provides benefits to the system, such as head loss reduction, pressure increase and pump energy consumption reduction. Finally, we apply the Shapley Value, a cooperative game theoretical framework, to estimate each players’ contribution to the water distribution system’s overall improvement.

Results

We use “epanettools” to test various network topologies. The results indicate that the location of the players in the network is crucial to the players’ subsidization. Specifically, the network topological characteristics, such as the distance between the Players and the water tank, need to be taken into consideration.

Conclusion:

Overall, our work illustrates that the Shapley Value can be used in order to assign subsidization values in water distribution network users and we provide a methodological framework and numerical examples.