| |
|
|
Abstract: In the Shapley--Scarf economy there are $n$ agents. Each one is endowed with one unit of an indivisible good (house) and wants to exchange it for another, possibly the most preferred one from the $n$ different houses in the market. In this economy, a core is always nonempty and a core allocation can be found by the famous Top Trading Cycles algorithm. Recently, a modification of this economy, containing $Q\ge 2$ types of goods (say, houses and cars for $Q=2$) has been introduced. We show that if the number of agents is 2, a complete description of the core can be found efficiently. However, when the number of agents is not restricted, the problem to decide the nonemptyness of the core becomes NP-hard. We also show that even the problem to decide whether an allocation exists in which each agent strictly improves compared to his endowment, is NP-complete. Contact the authors: katarina.cechlarova@upjs.sk Download PDF version of the preprint. |