Software price equilibrium under counterfeiting

The paper considers the market of software products. Regularly this markets are suffering from dealing with a problem of countefeit or pirate products that are sold. Taking this into account the paper is solving the problem of price equilibrium on this market. The software company set the price and the quality of the software product while the countefeit or pirate company suggest the consumers the product of the lower quality. First the general model is analyzed and price equilibrium is defined. Second, the monopoly case is considered separately and optimal software price is defined. Finally, it is supposed that there are two companies that produces original software on the market who differentiate in quality, and there are two pirate companies who produces this software. The duopoly case is analysed and equilibrium prices for competing companies are obtained in the explicit form.