Vertical cost information sharing in a supply chain with value-adding retailers

We consider a supply chain consisting of one supplier and two value-adding heterogeneous retailers. Each retailer has full knowledge about his own value-added cost structure that is unknown to the supplier and the other retailer. Assuming there is no horizontal information sharing between two retailers, we model the supply chain with a three-stage game-theoretic framework. In the first stage each retailer decides if he is willing to vertically disclose his private cost information to the supplier. In the second stage, given the information he has about the retailers, the supplier announces the wholesale price to the retailers. In response to the wholesale price, in the third stage, the retailers optimize their own retail prices and the values added to the product, respectively. Under certain conditions, we prove the existence of equilibrium prices and added values. Furthermore, we obtain the condition under which both retailers are unwilling to vertically share their private information with the supplier, as well as the conditions under which both retailers have incentives to reveal their cost information to the supplier, thus leading to a win-win situation for the whole supply chain.