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.