Feedback Nash Equilibria for Scalar Two-Player Linear-Quadratic Discrete-Time Dynamic Games

In this paper, we consider discrete-time, scalar, two-player, linear-quadratic dynamic games and study the coupled algebraic equations characterising feedback Nash equilibria. Using geometric arguments, we first analyse the possible number of distinct feedback Nash equilibrium solutions a game may admit and discuss properties of different solutions, before deriving conditions for the existence of no, one, two or three distinct feedback Nash equilibria. Finally, illustrative numerical simulations corroborate the theoretical findings. Copyright (c) 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)