A Game Model for Selecting a Seller’s Offer on the Marketplace

The interaction of buyers and sellers on the marketplace is formalized and studied. Each buyer forms an individual demand in the form of a vector of fuzzy characteristics of the necessary homogeneous product. In turn, each seller places a product offer for a homogeneous product in the form of a similar vector, but with clear values of characteristics, focusing on generalized customer demand and its own capabilities represented by a vector of fuzzy characteristics. The information contained in the vectors formed by the buyer and seller is available to the participants of the marketplace. The matching of the information content of these vectors determines the degree of their correspondence. The vector of characteristics of the coalition offer is introduced, which is a generalization of the offers of other sellers of this homogeneous product to the marketplace. The matching of the vector of the co-option offer and the fuzzy vector of the buyer determines the degree of their correspondence. A function is set, the values of which are interpreted as the probability of concluding a transaction. The game problem of choosing the offer of seller A by the criterion of the probability of making a transaction in competition with the coalition of other sellers in the marketplace is considered. The solution of a bimatrix game in mixed strategies is obtained. The strategies of seller A are a finite set of vectors with the proposed clear characteristics of the product, the strategies of the coalition B are a finite set of possible vectors of the coalition proposal with the linguistic values of the characteristic components. To calculate paired matches (game prices) in the matching process, operations with membership functions of fuzzy vector components, operators for aggregating the values of components of paired matches, models of generalized individual demand and coalition supply are used. A numerical example of a bimatrix game with recommendations for the formation of seller A’s proposals in the conditions of the random formation of the coalition B’s strategy is considered.