Cheap Talk Games with Two-Senders and Different Modes of Communication

We present a theoretical and experimental study of three Cheap Talk games, each having two senders and one receiver. The communication of senders is simultaneous in the first game, sequential in the second game and determined by the receiver in the third game (the Choice Game). We find that the overcommunication phenomenon observed in similar settings with only one sender becomes insignificant in our two-sender model regardless of the mode of communication. Despite similar theoretical predictions for these games, we observe systematic differences in experiments. In particular, while non-conflicting messages are observed less frequently under sequential communication due to the tendency of the second sender to revert the message of the first sender, the frequency of the second sender being truthful when the first sender lies is considerably higher in the Sequential Game in comparison to the truth-telling level in the Simultaneous Game. Moreover, in the Choice Game receiver prefers simultaneous mode of communication slightly more often than the sequential one. We explain the observed behavior of the players, estimating a logit quantal response equilibrium model and additionally running some logistic regressions. We find that the mode of communication is critical in design problems where a second opinion is available.