Envy-free solution and allocation rule of indivisible goods

Abstract

Given n indivisible goods and n agents we want to assign the goods among the agents, whose valuations on the goods determine the vector of prices. We prove that there always exists a solution that is envy-free and individually rational with non negative prices, under the assumption that agents have quasi - linear preferences on goods. Also, we provide an allocation rule that is strategy-proof and envy-free. Mathematics Subject Classication: 90C90, 91A12, 91B08, 91B26