Optimal control of trade discounts in a vertical distribution channel

We consider a vertical control distribution channel in which a manufacturer sells a single kind of good to a retailer. We assume that wholesale price discount increases the retailer's sale motivation thus improving sales. We first analyze the manufacturer's profit maximization problem as an optimal control model in which the manufacturer's control is the discount on wholesale price (trade discount). We then embed the model in a Stackelberg game environment considering that manufacturer and retailer can both be leader of the game, depending on the particular market structure.