We consider situations where a society allocates a finite units of an indivisible good among agents, and each agent receives at most one unit of the good. For example, imagine that a government allocates a fixed number of licences to private firms, or imagine that a government distributes...

We consider the problem of probabilistically allocating a single indivisible good among agents when monetary transfers are allowed. We construct a new strategy-proof rule, called the second price trading rule, and show that it is second best efficient. Furthermore, we give the second price...

I prove that there exists no assignment mechanism that is strategy-proof, non-wasteful and satisfies equal treatment of equals. This strengthens the impossibility result of Bogomolnaia and Moulin (2001) by weakening their assumption of ordinal efficiency to non-wastefulness. My result solves an...