Contract design in a cross-sales supply chain with demand information asymmetry

We examine a supply chain with two manufacturers in which each manufacturer implements a cross-sales strategy by selling a substitutable product through two common retailers. Both retailers face uncertain demands, and their demand forecasts are private. The manufacturers, as Stackelberg leaders, can decide whether or not to acquire this private information from the retailers through contract design: either a wholesale price contract without information sharing, or a two-part tariff contract with information sharing. We derive the Bayesian–Nash equilibriums for contract choice. We find that the two-part tariff contract can be a dominant choice under certain conditions. Specifically, with a lump sum payment set by the two manufacturers, both manufacturers and retailers can benefit from a two-part tariff contract if product package substitutability is more intensive and the demand uncertainty level is relatively high, or if the product package competition is less intense. They do not benefit from the two-part tariff contract, however, if product package substitutability is more intense and the demand uncertainty is relatively low. In addition, by comparing to the case in which the demand is deterministic, we find that a two-part tariff contract with shared information is more likely to benefit both manufacturers and both retailers than a wholesale price contract without information sharing. The implications of the contract choices are discussed.