Are you Going to Do That? Contingent-Payment Mechanisms to Improve Coordination

We consider simple coordination problems, such as allocating the right to use a shared sports facility or picking the time of a meeting. A mechanism selects an alternative in period zero based on reports from agents. This induces a decision problem for agents in period one; e.g., to use a resource, or to attend a meeting. Outcomes are designated as either good or bad, and the design goal is to maximize the probability of good outcomes (for example, maximize utilization or have enough people attend a meeting). Agents are self-interested, and have uncertainty about their value for different outcomes. An agent can choose whether to participate in the mechanism, what report to make in period zero, and which action to take in period one. We introduce the contingent second price mechanism (CSP), where reports in period zero are used to guide the principal’s decision and also to design contingent payments based on actions of agents in period one. For the single item resource allocation problem, we prove that under a mild assumption on agents’ value distributions, CSP mechanisms are straight-forward, meaning that each agent has a dominant strategy. Further, we prove that a full-revelation version of the mechanism maximizes utilization within a broad class of mechanisms. We also consider the meeting scheduling problem, where we show a dominant strategy equilibrium in a setting with two possible time slots. Interestingly, this is no longer the case for three or more time slots.