Competitive Equilibrium with Indivisibilities

This paper studies an exchange economy with a nite number of agents in which each agent is initially endowed with a nite number of (personalized) indivisible commodities. We observe that the equivalence theorem of the core and the competitive equilibrium may not hold for this economy when the coalitional form game is generated in the standard manner. We provide an alternative de nition of the coalitional form game to resolve this problem so that the balancedness of the new de ned game provides a useful necessary and su cient condition for the existence of competitive equilibrium for the original economy. We also observe that the nice strategy proof property of the minimum competitive price mechanism in the assignment problem and the Vickrey auction model does not carry over to the above economy. We show that examples of exchange economies exist for which no competitive price mechanism is individually (coalitionally) strategy proof. JEL classi cation numbers: D41, D44, D50 I thank Sushil Bikhchandani, Vince Crawford and editor Karl Shell for helpful comments and suggestions. I am grateful to an associate editor for many fruitful comments that greatly improve the exposition of the paper. Of course, any remaining errors are mine. Department of Economics, Rutgers University, Camden, NJ 08102, [email protected]