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arXiv · 2206.07102

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

Nathan Boyd·Steven Gabriel·George Rest·Tom Dumm
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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

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Nathan Boyd, Steven Gabriel, George Rest, Tom Dumm. 2022-06-14. Generalized Nash Equilibrium Models for Asymmetric, Non-cooperative Games on Line Graphs: Application to Water Resource Systems. https://arxiv.org/abs/2206.07102

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