Dynamic Allocation without Money

We analyze the optimal design of dynamic mechanisms in the absence of transfers. The agent’s value evolves according to a two-state Markov chain. The designer uses future allocation decisions to elicit private information. We solve for the optimal allocation mechanism. Unlike with transfers, efficiency decreases over time. In the long run, polarization occurs. A simple implementation is provided. The agent is endowed with a “quantified entitlement,” corresponding to the number of units he is entitled to claim in a row