Strategy-proof and envyfree random assignment
We study the random assignment of indivisible objects among a set of agents with strict preferences. We show that there exists no mechanism which is strategy-proof, envyfree and unanimous. Then we weaken the latter requirement to q-unanimity: when each agent ranks a different object at the top, then any agent shall receive his most preferred object with probability of at least q. We show that if a mechanism satisfies strategyproofness, envyfreeness, ex-post weak non-wastefulness, ex-post weak efficiency and q-unanimity, then q must be smaller than or equal to 2 |N| (where |N| is the number of agents). We introduce a new mechanism called random careless dictator (RCD) and show that RCD achieves this maximal bound. In addition, for three agents, RCD is characterized by the first four properties. JEL Classification: D63, D70.
Random assignment Strategy-proofness Envyfreeness q-unanimity