Dynamic Games with Strategic Complements and Large Number of Players

We study dynamic games with strategic complements where each player is modeled by a scalar flow dynamical system with a controlled input and an uncontrolled output. The model originates in inventory control problems with shared set-up costs and a large number of players. An activation cost is shared among active players, namely players who control their dynamics at a given time. As a main contribution, we prove that two-threshold strategies, like the (s, S) strategies used in inventory control, are mean-field equilibrium strategies in dynamic games with a large number of players. Furthermore, we provide conditions for the convergence of the nonstationary mean-field equilibrium to the stationary one in the limit.