Competitive Equilibria in a Market for Indivisible Commodities with Middlemen

In this paper, we consider a market of indivisible goods with middlemen as an assignment market. Initially, we show that the set of all imputations given by competitive equilibria of an assignment market with middlemen who trade a single unit of indivisible goods coincides with the core of the game derived from the market. Next, by using the first result, we show that the set of all imputations given by competitive equilibria of an assignment market with middlemen who trade multiple units of indivisible goods coincides with the core of the game of another three-sided assignment market generated from this market. Finally, by using the second result, we give an equivalent condition for the existence of a competitive equilibrium of an assignment market in which each middleman trades multiple units of goods. This equivalent condition can be characterized by the existence of an integral solution of a linear program.