Random priority item allocation
Random priority (RP), also called Random serial dictatorship (RSD), is a procedure for fair random assignment - dividing indivisible items fairly among people. Suppose partners have to divide (or fewer) different items among them. Since the items are indivisible, some partners will necessarily get the less-preferred items (or no items at all). RSD attempts to insert fairness into this situation in the following way. Draw a random permutation of the agents from the uniform distribution. Then, let them successively choose an object in that order (so the first agent in the ordering gets first pick and so on). Properties RSD is a truthful mechanism when the number of items is at most the number of agents, since you only have one opportunity to pick an item, and the obviously dominant strategy in this opportunity is to pick the best available item. RSD always yields an ex-post Pareto efficient (PE) outcome. Moreover, in an assignment problem, every deterministic PE assignment is the outcome of SD for some ordering of the agents. However, RSD is not ex-ante PE when the agents have Von Neumann-Morgenstern utilities over random allocations, i.e., lotteries over objects (Note that ex-ante envy-freeness is weaker than ex-post envy-freeness, but