A coordination problem exists when assigning resources or tasks to agents. Consider assigning spaces in a spinning class for example, or time slots for a neighborhood electric vehicle recharging station, or shifts to volunteers in a child care co-op. In each case, the assignment decision is associated with an intended action and the problem is to coordinate about future actions in the presence of uncertainty, self interest and private information. Coordination success or failure depends on follow-through by agents (e.g., attending the spinning class or not, using the charging station or not, showing up for the assigned shift or not). We want to maximize the probability that agents adopt their assigned role (e.g., maximizing the expected number of agents who attend the spinning class, use the charging station, or show up to the co-op at designated times).
In our model, each agent has private information about its value distribution for different assignment. A mechanism elicits information about value distributions, using this information to determine an assignment along with payments, including payments that are contingent on an agent's future action. Once assigned, each agent later realizes its value and decides how to act. We seek dominant strategy, no deficit mechanisms with voluntary participation, that maximize the expected number of agents who adopt the intended action subject to a natural design constraints. For allocating a single resource, we propose a contingent second-price (CSP) mechanism, prove that CSP is unique under a set of desired criteria, and that CSP is optimal across a larger class of mechanisms. We extend the mechanism to assigning multiple, identical resources (the spinning class) and multiple, heterogeneous resources (charging station, co-op shifts), providing theoretical and experimental justification for the performance of generalized CSP mechanisms.