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 who have to be assigned items at each date. When the social planner can only elicit ordinal agents' preferences, we prove that under a mild regularity assumption, incentive compatible and ordinally efficient allocation rules coincide with spot mechanisms. The latter specify "virtual prices" for items at each date and, for each agent, randomly selects a budget of virtual money at the beginning of time. When the social planner can elicit cardinal preferences, we prove that under a similar regularity assumption, incentive compatible and Pareto efficient mechanisms coincide with Spot Menu of Random Budgets mechanisms. These are similar to spot mechanisms except that, at the beginning of time, each agent chooses within a menu, a distribution over budget of virtual money.