Existence and uniqueness of open-loop Nash equilibria in linear-quadratic discrete time games

We present existence and uniqueness results for an equilibrium in an M-person Nash game with quadratic performance criteria and a linear difference equation as constraint, describing the system dynamics under an open-loop information pattern. The approach used is the construction of a value function which leads to existence assertions in terms of solvability of certain symmetric and nonsymmetric Riccati difference equations.