This article deals with the problem of improving the effectiveness of a marketplace. The stakeholders of a marketplace are buyers and sellers. The objects are the aggregate of homogeneous products. The effectiveness of the trading platform, which can be characterized by the number of transactions made, will depend on how sufficiently the sellers put up offers. The paper looks at mathematical models to support the decision-making of the seller in making such offers. Focusing not only on the buyer demand but also on the presence of competitors on the site is a distinguishing feature of the models. To describe the competition, the apparatus of game theory is offered, namely the normal form of the game with a bimatrix model with two players: the seller – customer of service and the coalition of other sellers. To match offer and demand, as well as to find the probability of a transaction, fuzzy set theory and aggregation using the Choquet integral are used.