Knowing who speaks when: On commonly known consensus∗

We study a model of pairwise communication in a finite population of Bayesian agents. We show that, in contrast with claims to the contrary in the existing literature, communication under a fair protocol may not lead to commonly known signals, or even consensus. We prove that, in order for commonly known signals to be achieved, individuals must also know the structure of the communication protocol. In this case, a consensus will be also reached. JEL Codes: D82, D89. ∗We would like to thank Amanda Friedenberg, John Geanakoplos, Andrew Postlewaite, Fernando Vega-Redondo, Alpaslan Akay, and the participants in the 6th Conference on Research on Economic Theory and Econometrics, Naxos, Greece for fruitful discussions and comments. Financial support from the Netherlands Organization for Scientific Research (NWO), the Wallander/Hedelius Foundation, and the Adlerbertska Forskningsstiftelsen Foundation is gratefully acknowledged. Tsakas thanks the Stockholm School of Economics for its hospitality while working on this paper. †Tel:+46-31-786 4106; Fax:+46-31-786 4154; E-mail: [email protected] ‡Tel:+46-8-736 9217; Fax:+46-8-31 32 07; E-mail: [email protected]