Private communication in competing mechanism games

We study games in which principals simultaneously post mechanisms in the presence of several agents. We evaluate the role of principals’ communication in these settings. As in Myerson (1982), each principal may generate incomplete information among agents by sending them private signals. We show that this channel of communication, which has not been considered in standard approaches to competing mechanisms, has relevant strategic effects. Specifically, we construct an example of a complete information game in which (multiple) equilibria are sustained as in Yamashita (2010) and none of them survives in games in which all principals can send private signals to agents. The corresponding sets of equilibrium allocations are therefore disjoint. The role of private communication we document may hence call for extending the construction of Epstein and Peters (1999) to incorporate this additional element.