Trading higher software piracy for higher profits: the case of phantom piracy

This paper analytically explores the effect of software bundling on software piracy. We focus on piracy at individual user level where several individuals illegitimately share a single copy of software. We develop an economic model of software piracy with bundling of two products that are not identically distributed. We derive results for optimal level of piracy and profits for individual products as well as for the bundle. Our results indicate that bundling results in a level of piracy that is always less than the piracy level of one of the products of the bundle. However, it is possible to trade off the piracy level of one product for overall higher profits, i.e., a seller can derive higher profits even with higher levels of piracy for one of the products in the bundle. We derive exact bounds for two cases: (i) where piracy level of the bundle is smaller than the piracy level of both the products in the bundle, and (ii) where the profits from a bundle are always higher even with higher piracy level than one of the products.