  In this paper, we consider a discrete-time stochastic Stackelberg game with a
single leader and multiple followers. Both the followers and the leader
together 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 the
leader commits to a dynamic strategy. Each follower's strategy is the best
response to the leader's strategies and other followers' strategies while the
each leader's strategy is optimum given the followers play the best response.
In general, computing such equilibrium involves solving a fixed-point equation
for the whole game. In this paper, we present a backward recursive algorithm
that computes such strategies by solving smaller fixed-point equations for each
time $t$. Based on this algorithm, we compute stochastic Stackelberg
equilibrium of a security example and a dynamics information design example
used in~\cite{El17} (beeps).
