Stochastic Stackelberg games

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). Both attacker and defender have conditionally independent private types, conditioned on action and previous state, that evolve as controlled Markov processes. 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 smaller fixed-point equations for each time $t$. This reduces the computational complexity of the problem from double exponential in time to linear in time. Based on this algorithm, we compute stochastic Stackelberg equilibrium of a security example.