Optimal price and maximum deal size on group-buying websites for sellers with finite capacity

This paper presents an analytical model for sellers with finite capacity to optimise their price and maximum deal size limit on group-buying websites. For the general demand functions that satisfy some mild regularity conditions, the optimal strategies and the corresponding deal parameters are characterised. The optimal strategies demonstrate that deep online discounts (selling products below the cost or even selling products for free) can be optimal if the maximum deal size is used strategically. Moreover, deep discounts can be beneficial even if the capacity is tight, which explains the use of deep discounts commonly observed in practice. Our results also provide the operators of group-buying websites with useful suggestions on how to induce sellers to offer deep discounts. Sensitivity analysis with regard to the minimum deal size and capacity is provided. Our analysis shows that counter-intuitively selling out capacity may not always be optimal, even if the amount of capacity cannot satisfy the unconstrained optimal sales quantity online. Finally, we extend the model to consider offline prices being sellers’ decisions and discuss the robustness of the optimal strategies when the demand is stochastic.