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.