Optimal order policies for supply chain with options contracts

We consider two independent retailers that face stochastic demand. Because of long lead-time and short selling season, retailers obtain goods from a supplier via options contract. At the beginning of the selling season, retailer can adjust their positions by trading options with another when the demand is realized. We focus on deriving how the possibility of such options trading between two independent retailers affects each retailer's optimal order and optimal profit. Game theory is adopted as an analysis tool. We show that there exists a unique Nash equilibrium in pure strategy for retailers' optimal orders with options trading. The retailer's optimal profit with options trading is higher than the case without options trading. The retailers' optimal orders with options trading all increase in options trading price. There exists a unique optimal options price that yields the retailers' joint optimal profit.