On the Shapley-Scarf economy: the case of multiple types of indivisible goods

We study a generalization of Shapley-Scarfs [Journal of Mathematical Econom ics 1 (1974) 23-37] economy in which multiple types of indivisible goods ar e traded, We show that many of the distinctive results from the Shapley-Sca rf economy do not carry over to this model, even if agents' preferences are strict and can be represented by additively separable utility functions. T he core may be empty. The strict core, if nonempty, may be multi-valued, an d might not coincide with the set of competitive allocations, Furthermore, there is no Pareto efficient, individually rational, and strategy-proof soc ial choice rule. We also show that the core may be empty in the class of ec onomies with a single type of indivisible good and agents consuming multipl e units, even if no complementarity exists among the goods. (C) 2001 Elsevi er Science B.V. All rights reserved.