With a novel search algorithm or assortment planning or assortment optimization algorithm that takes into account a Bayesian approach to information updating and two-stage assortment optimization techniques, the current research provides a novel concept of competitiveness in the digital marketplace. Via the search algorithm, there is competition between the platform, vendors, and private brands of the platform. The current paper suggests a model and discusses how competition and collusion arise in the digital marketplace through assortment planning or assortment optimization algorithm. Furthermore, it suggests a model of an assortment algorithm free from collusion between the platform and the large vendors. The paper's major conclusions are that collusive assortment may raise a product's purchase likelihood but fail to maximize expected revenue. The proposed assortment planning, on the other hand, maintains competitiveness while maximizing expected revenue.