Multidimensional cheap talk with sequential messages

Abstract

This paper studies a two-dimensional cheap talk game with two senders and one receiver. The senders possess the same information and sequentially send messages about that information. In one-dimensional sequential message cheap talk games where the state space is unbounded, the information is fully transmitted under the self-serving belief, as suggested by Krishna and Morgan (2001b). However, this result depends crucially on the structure of the one-dimensional model. It generally does not hold in two-dimensional models. We consider the extended self-serving belief, which implies full information transmission even if the self-serving belief cannot work. Then, we show that the necessary and sufficient condition for the existence of the fully revealing equilibrium is that the senders have opposing-biased preferences.