An Envy-free Pricing Algorithm for Multi Item Market with Covering Constraints

In recent years, with the spread of personal computers and smartphones, the advertisement distribution market through the Internet is growing. Most of the advertisement distribution service is a listing advertisement displayed in accordance with attributes of users and search words. One of an interest topic of item allocation and pricing problem is an envy-freeness. A key idea of envy-free is that no buyer has incentive to exchange own items and its payment pair with another buyer's items and its payment pair. It is known that a revenue maximization problem with envy-freeness is a NP-hard problem. In this paper, we study a special case of multi items envy-free allocation problems. Every buyer has a unit valuation, a budget and a preferred item set the buyer wants.