Random assignment of multiple indivisible objects

We consider random assignment of multiple indivisible objects. When each agent receives one object, Bogomolnaia and Moulin (2001) show that the probabilistic serial mechanism is ordinally efficient, envy-free and weakly strategy-proof. When each agent receives more than one object, we propose a generalized probabilistic serial mechanism that is ordinally efficient and envy-free but not weakly strategy-proof. Our main result shows that, if each agent receives more than one object, there exists no mechanism that is ordinally efficient, envy-free and weakly strategy-proof. JEL Classification Numbers: C70, D61, D63.