Online platforms have been expanding the seller base to widen their product assortment to match the individual preferences of consumers. Nevertheless, the increasing number of sellers leads to intensified competition and results in sellers setting lower prices for the products. Thus, it is unclear whether displaying all the sellers to the entire customer base maximizes platform revenue. Motivated by the unique setting of Airbnb, we consider a game theoretical setup in which each seller on the platform provides a single-unit product and competes with one another on price. We investigate sellers' optimal pricing decisions and the platform’s optimal assortment display policy, which is characterized by the partitioning of products and traffic assigned to each partition. We find that the platform should display the entire assortment to all the customers when demand is sufficiently high. Moreover, we propose a tabulation algorithm and a mixed-integer programming formulation to effectively solve for the sellers' and the platform’s optimal decisions. Additionally, we incorporate constraints on the closeness of different metrics among partitions in our formulation to guarantee a certain degree of fairness in the optimal display policy. Specifically, we introduce $(\alpha,\delta)$-fairness and envy level to measure sellers fairness, and $\gamma$-fairness to gauge customers fairness. Using data from Airbnb, we present a case study to illustrate how our model framework can be applied in practice. Finally, we extend the case in which each seller supplies a distinct product with inventory size of one by considering scenarios in which each product has more than one unit.