Dynamic Mechanism Design without Money

Abstract

In this dissertation, we study settings where a principal repeatedly determines the allocation of a single resource to i) a single agent, ii) one of two agents, and iii) one of n agents without monetary transfers over an infinite horizon with discounting. In all settings, the value of each agent for the resource in each period is private and the value distribution is common knowledge. For these settings, we design dynamic mechanisms that induce agents to report their values truthfully in each period via promises/threats of future favorable/unfavorable allocations. We show that our mechanisms asymptotically achieve the first-best efficient allocation (the welfare-maximizing allocation as if values are public) as the discount factor increases. Our results provide sharp characterizations ofconvergence rates to first best as a function of the discount factor.In the single-agent setting, the principal incurs a positive cost from allocating the resource to the agent. We first consider the case in which the allocation cost is random in each period with a known distribution. Next, we extend the model such that the allocation cost follows one of two possible probability distributions. The principal and the agent share the same belief about the true cost distribution and update their beliefs in each period using Bayes’ rule. In both cases, we provide mechanisms whose convergence rates are optimal, i.e., no other mechanism can converge faster to first best. In the settings with two or more agents, we do not consider allocation cost. We study the two-agent case before extending it to n agents. For two agents, we prove that the convergence rate of our mechanism is optimal. For n agents, we provide the convergence rate of our mechanism as a function of n.