Mechanism Design for Optimal Consensus Problems

We consider stationary consensus protocols for networks of dynamic agents with switching topologies. At each time instant, each agent knows only its and its neighbors' state, but must reach consensus on a group decision value that is function of all the agents' initial state. We show that our protocol design is the solution of individual optimizations performed by the agents. This notion suggests a game theoretic interpretation of consensus problems as mechanism design problems. Under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives. We prove that such objectives can be chosen so that rational agents have a unique optimal protocol, and asymptotically reach consensus on a desired group decision value