Dynamic assignment without money: Optimality of spot mechanisms

We study a large market model of dynamic matching with no monetary transfers and a continuum of agents. Time is discrete and horizon finite. Agents are in the market from the first date and, at each date, have to be assigned items (or bundles of items). When the social planner can only elicit ordinal preferences of agents over the sequences of items, we prove that, under a mild regularity assumption, incentive compatible and ordinally efficient allocation rules coincide with spot mechanisms. A spot mechanism specifies “virtual prices” for items at each date and, at the beginning of time, for each agent, randomly selects a budget of virtual money according to a (potentially non-uniform) distribution over [0,1]. Then, at each date, the agent is allocated the item of his choice among the affordable ones. Spot mechanisms impose a linear structure on prices and, perhaps surprisingly, our result shows that this linear structure is what is needed when one requires incentive compatibility and ordinal efficiency. When the social planner can elicit cardinal preferences, we prove that, under a similar regularity assumption, incentive compatible and Pareto efficient mechanisms coincide with a class of mechanisms we call Spot Menu of Random Budgets mechanisms. These mechanisms are similar to spot mechanisms except that, at the beginning of the time, each agent must pick a distribution in a menu. This distribution is used to initially draw the agent's budget of virtual money.