Stackelberg equilibria for discrete-time dynamic games part I: Deterministic games

We consider a two-person discrete-time dynamic game with the prespecified fixed duration. Each player maximizes her profit over the game horizon, taking decisions of the other player into account. Our goal is to find the Stackelberg equilibria for such a game. The solution approach differs with respect to the information available to individual players. While in the game with open-loop information structure the solution procedure is straightforward and already reported in the literature, the problem with the closed-loop problem information structure is difficult to solve, especially if twice differentiability of the leader's strategy is not imposed a priori. In this paper we focus on deterministic problems. We review classical optimization methods that can be used to solve the games with open-loop information structure. Additionally, we propose new methods for solving the games with the closed-loop information structure. Application of such methods is shown on specific examples. In the companion paper (Stackel-berg Equilibria for Discrete-Time Dynamic Games — Part II: Stochastic Games with Deterministic Information Structure) we will consider a stochastic variant of the problem.