Incentives for a Retailer with Two-Dimensional Asymmetric Information

We study a two-tier supply chain where a manufacturer faces a retailer privileged with private information about both the forecast signal and its accuracy from contracting before and after the retailer's forecast two aspects. To better understand the impact of these two types of asymmetric information, four information structures are investigated: no asymmetric information, only forecast signal is asymmetric information, only forecast accuracy is asymmetric information and both forecast signal and its accuracy are asymmetric information. It demonstrates that for all these four cases, the optimal incentive schemes designed for the retailer take on a threshold structure of the unit production cost. Meanwhile, contrary to the intuition and previous findings, we find that the high precision level forecast is not always the manufacturer's preference, which rests not only with the observed signal, but also with the manufacturer's unit production cost and the retailer's cost-efficiency of making a high precision level forecast. And more importantly, it shows that more private information (two-dimensional asymmetric information or one asymmetric information) does not necessarily make the retailer better off or make the manufacturer worse off, which depends on the values of the parameters such as the retailer price, the demand level, the manufacturer's belief about the retailer's private information, etc. Besides, for the same asymmetric information, the values of information on the specific information may be different. Finally, the value of contracting sequence is explored. And it indicates that no matter what the information structure is, contracting after the retailer's forecast is always more attractive to the manufacturer, whereas contracting before the retailer's forecast is more attractive to the retailer.