DOI 10.1007/s11238-005-6013-7 Theory and Decision (2006) 61: 63–74 © Springer 2006 RYUICHIRO ISHIKAWA COMMUNICATION PROTOCOLS WITH BELIEF MESSAGES ABSTRACT. This paper presents a communication protocol to reach consensus. In our setting, every player has asymmetric information and evaluates a fixed event on his information. According to the protocol, the sender sends non-partitional messages that he believes the event with a probability of at least his evaluation. We show that the posteriors for the event must be equal among the players after the communication. Journal of Economic Literature Classification: C62, C78. KEY WORDS: communication, protocol, p-belief, consensus, agreeing to disagree 1. INTRODUCTION This paper shows a repetitive process to reach consensus through communications with belief messages. In our set- ting, players have asymmetric information and evaluate the occurrence of a fixed event by a probability based on his information. According to a protocol, each of them sends the messages of the evaluation each other. Then, we have the result that all the players reach an identical probability for the given event through the repetitive process. The belief messages they communicate are the evaluations over the minimal probabilities. That is, each sender communi- cates the message that he believes the event with a probability of at least his evaluation. The construction of these messages is similar to p-beliefs of Monderer and Samet (1989) and therefore, these messages are not partitions of a state space. Nevertheless, the essential difference is to change players’ minimal probabilities unlike p of p-beliefs. This reflects that the players’ private information may be changed or revised.