Stackelberg equilibria for discrete-time dynamic games part II: Stochastic games with deterministic information structure

We consider a two-person discrete-time dynamic game with a 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. After having discussed deterministic Stackelberg games in the companion paper (Stackelberg Equilibria for Discrete-Time Dynamic Games — Part I: Deterministic Games), in this paper we focus on stochastic games with a deterministic information structure. While for the stochastic game with open-loop structure the solution procedure is straightforward and already reported in the literature, the problem with the closed-loop problem information structure for stochastic games remains a challenge. After discussing a rather standard approach to solve the open-loop stochastic game, we propose an approach to find (sub)optimal solutions of the closed-loop game. Moreover, we discuss solution approach for generalized games in which the leader has access to the follower's past actions, the so-called inverse Stackelberg games.