Consensus, communication and knowledge: An extension with Bayesian agents

Parikh and Krasucki [Parikh, R., Krasucki, P., 1990. Communication, consensus and knowledge. Journal of Economic Theory 52, 178-189] showed that pairwise communication of the value of a function f leads to a consensus about the communicated value if the function f is convex. They showed that union consistency of f may not be sufficient to guarantee consensus in any communication protocol. Krasucki [Krasucki, P., 1996. Protocols forcing consensus. Journal of Economic Theory 70, 266-272] proved that consensus occurs for any union consistent function if the protocol contains no cycle. We show that if agents communicate their optimal action, namely the action that maximizes their expected utility, then consensus obtains in any fair protocol for any action space.