In this paper, we consider a discrete-time stochastic Stackelberg game where there is a defender (also called leader) who has to defend a target and an attacker (also called follower). The attacker has a private type that evolves as a controlled Markov process. The objective is to compute the stochastic Stackelberg equilibrium of the game where defender commits to a strategy. The attacker’s strategy is the best response to the defender strategy and defender’s strategy is optimum given the attacker plays the best response. In general, computing such equilibrium involves solving a fixed-point equation for the whole game. In this paper, we present an algorithm that computes such strategies by solving lower dimensional fixed-point equations for each time t. Based on this algorithm, we compute the Stackelberg equilibrium of a security example.

2022 American Control Conference (ACC)