We consider a manufacturer that has a capacity constraint and allocates capacity according to the lexicographic mechanism, which involves assigning different priority levels to different retailers. The manufacturer sells products to two competing retailers: a high-priority one and a low-priority one. The manufacturer's capacity information is either public or private, which makes our paper the first to examine the impact of capacity information on the capacity allocation problem of a manufacturer. We investigate two contract types: wholesale-price and wholesale-price-and-quantity. Our results show that when capacity information is public, the manufacturer will always prefer a wholesale-price contract. Moreover, it can benefit from a lower capacity limit (capacity scarcity) due to the retailer's capacity-withholding behavior. Interestingly, the high-priority retailer may prefer that the manufacturer use a wholesale-price-and-quantity contract to limit how many items the retailer can order. When capacity information is private, the retailer can order more than the capacity of a low-type manufacturer to reveal the manufacturer's capacity level under the wholesale-price contract. At the same time, under a wholesale-price contract, the manufacturer may not want to supply all the order quantities to the retailers to avoid disclosing its capacity level. We find that pooling equilibrium can survive the Intuitive Criterion, and the manufacturer cannot benefit from capacity scarcity and withholding no longer occurs. Lastly, contrary to the case where capacity information is public, the manufacturer may prefer the wholesale-price-and-quantity contract when capacity information is private. Therefore, it is possible to achieve a win-win situation between supply chain partners with the right contract type, which is not possible when capacity information is public.

我们考虑一个制造商，它有产能限制并根据词典机制分配产能，这涉及为不同的零售商分配不同的优先级。制造商将产品销售给两个相互竞争的零售商：一个高优先级零售商和一个低优先级零售商。制造商的产能信息要么是公开的，要么是私有的，这使得我们的论文首次检验了产能信息对制造商产能分配问题的影响。我们调查了两种合同类型：批发价格和批发价格加数量。我们的结果表明，当容量信息公开时，制造商总是更喜欢批发价合同。此外，由于零售商的容量限制行为，它可以受益于较低的容量限制（容量稀缺）。有趣的是，高优先级零售商可能更愿意制造商使用批发价格和数量合同来限制零售商可以订购的商品数量。当产能信息保密时，零售商可以订购比低类型制造商更多的产能，以揭示批发价合同下制造商的产能水平。同时，在批发价合同下，制造商可能不想向零售商供应所有订单数量，以避免泄露其产能水平。我们发现合并均衡可以在直觉准则下存活，并且制造商无法从产能稀缺中获益并且不再发生预扣。最后，与产能信息公开的情况相反，当产能信息私有时，制造商可能更喜欢批发价格和数量合同。