Before revision:  We then establish that long-run average optimality can be maintained by optimizing over a class of joint information design and promotion policies under which the platform provides the seller with a (random) information signal at the beginning of the horizon, and then uses the best confounding promotion policy, which prevents the sellerfrom further learning. Additionally, we show that myopic pricing is a best response to such a platformstrategy, thereby establishing an approximate Bayesian Nash equilibrium between the platform and the seller .
After revision:  We then establish that long-run average optimality can be maintained by optimizing over a class of joint information design and promotion policies when the seller sets prices myopically. We then establish a Bayesian Nash equilibrium by showing that the seller's best response to such a platformstrategy, thereby establishing an approximate Bayesian Nash equilibrium between the platform and the seller .