Abstract: Capacity constraint is a common problem in supply chain. In reality, enterprises' capacity constraints are caused by many factors, such as the shortage of raw materials or spare parts, complicated production processes or backward technologies, and infectious diseases, but the final results are limited capacity. At the same time, there is also information asymmetry among the member enterprises of the supply chain, which is not only easy to lead to the imbalance of decision-making incentive of the supply chain, but also may exacerbate the adverse impact of capacity constraint on the supply chain. In this paper, it is considered that a supply chain consisting of a brand manufacturer who has limited capacity and a retailer. The retailer has private information about the consumers' mismatch cost. The optimal price decisions and contracts design under asymmetric information are analyzed. Further, the optimal decisions of both the brand manufacturer and the retailer under full information and asymmetric information are derived and compared.
The main work in this paper includes four parts. At first, optimal contracts are proposed and the optimal pricing strategies and contract design under full information and asymmetric information are analyzed, respectively. Second, on this basis, the best contract option for the brand manufacturer under three types of wholesale contracts and the effects of the wholesale contract selection on the product demand is analyzed. Third, the optimal decisions of both the brand manufacturer and the retailer under full information and asymmetric information are compared. And the effect of wholesale contract selection on the information value of the supply chain enterprises and supply chain system. Finally, the information sharing policies between brand manufacturer and the retailer under three types of wholesale contracts is presented.
The results show that, the two-part tariff contracting scheme, composed of a wholesale price and a fixed payment, can coordinate the supply chain perfectly under full information. By solving the optimization problem, the low wholesale price strategy, the fixed wholesale price strategy and the high wholesale price strategy for the brand manufacturer are presented under asymmetric information, respectively. By comparing and analyzing the profits of the brand manufacturer under the three types of wholesale contracts, it is further found that the brand manufacturer should choose low-price contract or high-price contract according to different market conditions, instead of fixed-price contract. The brand manufacturer's profit will be less due to lack of accurate information about consumer personal information leakage risk cost, while the asymmetry information may not decrease the profit of the whole supply chain or generates extra information rent. Moreover, when the brand manufacturer's bargaining power satisfy certain conditions under the high wholesale price strategy, the online retailer will reveal the private information voluntarily and share the supply chain's profit with the brand manufacturer.
In summary, the optimal price decisions and contracts design under capacity constraints are studied by employing game theory. The findings in this paper can provide academic and practical insights for supply chain collaboration.

Key words: capacity constraints, contracts design, asymmetric information, pricing