Generalized Nash Equilibrium Models for Asymmetric, Non-cooperative Games on Line Graphs: Application to Water Resource Systems

TL;DR

This paper develops a generalized Nash equilibrium model for asymmetric, non-cooperative games on line graphs, applied to water resource systems, aiming to reduce inequitable benefits among players.

Contribution

It introduces a realistic, non-cooperative game-theoretic approach for resource allocation on line graphs, specifically applied to water management in river basins.

Findings

Water-release market can be an effective policy instrument.

Model reduces asymmetry in resource benefits.

Application to real water systems demonstrates practical relevance.

Abstract

This paper investigates the game theory of resource-allocation situations where the "first come, first serve" heuristic creates inequitable, asymmetric benefits to the players. Specifically, this problem is formulated as a Generalized Nash Equilibrium Model where the players are arranged sequentially along a directed line graph. The goal of the model is to reduce the asymmetric benefits among the players using a policy instrument. It serves as a more realistic, alternative approach to the line-graph models considered in the cooperative game-theoretic literature. An application-oriented formulation is also developed for water resource systems. The players in this model are utilities who withdraw water and are arranged along a river basin from upstream to downstream. This model is applied to a stylized, three-node model as well as a test bed in the Duck River Basin in Tennessee, USA. Based on the results, a non-cooperative, water-release market can be an acceptable policy instrument according to metrics traditionally used in cooperative game theory