This work presents a linear programming model for virtual markets. The main objective is to encourage sellers to offer lower prices and buyers to pay more for products. This is done through a system where the agents are awarded for acting this way. The basic version of the model works as an auction where buyers and sellers can make their bids. Some extensions were developed for this basic model, to allow situations like: transportation cost between buyers and sellers; scale economy for the buyer's price; multiples products in the same auction. For the basic model and each of its extensions, the system of awards has been developed based on Game Theory principles. In each case, the model was reinterpreted as a game and its core solutions were found. It was also verified how these solutions determine market's behavior.