A Pseudo-Code for Algorithms Algorithm 2 Value Iteration (with Min-Max Oracle) Inputs: S, X, Y,r, g,p,, T Outputs: v (T) 1: Initialize v (0) arbitrarily, e.g. v

X, Y are compact sets. Assumption 1.1, C is a contraction mapping w.r .t. to the sup norm k . By combining Theorem 2.3 and the Banach fixed point theorem [57], we First note that by Assumption 1.1, we have that Suppose that Assumption 1.1 holds, and that 1. for all Suppose that Assumption 1.1 holds, and that 1. for all By Theorem 2.1 and Theorem 2.3 we know that The proof follows exactly the same, albeit the optimality conditions on the inner player's policy By Theorem 3.1, the necessary optimality conditions for the stochastic Stackelberg game are that for all states This reduced the market to a deterministic repeated market setting in which the amount of budget saved by the buyers differentiates different states of the market. As a result, we had to use fitted variant of value iteration. This time, we implemented a stochastic transitions.