Multidimensional Evolution Effects on Non-Cooperative Strategic Games

Shipra Singh, Aviv Gibali () and Simeon Reich
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Shipra Singh: Department of Electric Energy, Norwegian University of Science and Technology, 7034 Trondheim, Norway
Aviv Gibali: Department of Applied Mathematics, HIT Holon Institute of Technology, 52 Golomb Street, Holon 5810201, Israel
Simeon Reich: Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 3200003, Israel

Mathematics, 2024, vol. 12, issue 16, 1-30

Abstract: In this study, we examine how the strategies of the players over multiple time scales impact the decision making, resulting payoffs and the costs in non-cooperative strategic games. We propose a dynamic generalized Nash equilibrium problem for non-cooperative strategic games which evolve in multidimensions. We also define an equivalent dynamic quasi-variational inequality problem. The existence of equilibria is established, and a spot electricity market problem is reformulated in terms of the proposed dynamic generalized Nash equilibrium problem. Employing the theory of projected dynamical systems, we illustrate our approach by applying it to a 39-bus network case, which is based on the New England system. Moreover, we illustrate a comparative study between multiple time scales and a single time scale by a simple numerical experiment.

Keywords: game theory; dynamic generalized Nash equilibrium problem; dynamic quasi-variational inequality problem; spot electricity market problem; projected dynamical system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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