In this paper, we examine a supply chain in which a single supplier sells to a downstream retailer. We consider a multiperiod model with the following sequence of events. In period t the supplier offers a contract to the retailer, and the retailer makes her purchasing decision in anticipation of the random demand. The demand then unravels, and the retailer carries over any excess inventory to the next period (unmet demand is lost). In period t 1 the supplier designs a new contract based on his belief of the retailer's inventory, and the game is played dynamically. We assume that short-term contracts are used, i.e., the contracting is dynamically conducted at the beginning of each period. We also assume that the retailer's inventory before ordering is not observed by the supplier. This setting describes scenarios in which the downstream retailer does not share inventory/sales information with the supplier. For instance, it captures the phenomenon of retailers distorting past sales information to secure better contracting terms from their suppliers. We cast our problem as a dynamic adverse-selection problem and show that, given relatively high production and holding costs, the optimal contract can take the form of a batch-order contract, which minimizes the retailer's information advantage. We then analyze the performance of this type of contract with respect to some useful benchmarks and quantify the value of prudent contract design and the value of inventory information to the supply chain. Markovian adverse-selection models, in which the state and action in a period affect the state in the subsequent period, are recognized as theoretically challenging and are relatively less understood. We take a nontrivial step towards a better understanding of such models under short-term contracting.
