In this paper, we consider modern loyalty programs that use CRM (Customer Relationship Management). Ordinary discount cards do not allow to fully manage repeated touches with customers. The main task of the seller is to find ways to keep customers coming back. There are encouraged to use mathematical modeling using the game theory. This will allow the seller and the buyer to find the best strategies. In addition, the possibility of finding the best strategies of the seller in case of a change in the matrix of profits due to certain circumstances is considered. In this case, the behavior of the customers flow is given by a highly likely mixed strategy.

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