Two-sided communication in competing mechanism games

We consider multiple-principal multiple-agent games of incomplete information. We identify a class of two-way communication mechanisms which mirror those considered in the single principal analysis of Myerson (1982). In such mechanisms, every agent truthfully reveals her type to all principals, and obeys the private recommendations she receives from each of them. We show that there is a rationale in restricting attention to this class of mechanisms: if principals use these mechanisms, there is no unilateral incentive to deviate towards more sophisticated ones. We develop three examples to analyze possible extensions and limits of our approach. The first two examples show that the restriction to direct and incentive compatible mechanisms is not sufficient to provide a complete characterization of all pure strategy equilibria. The third one shows that private recommendations play a fundamental role in competing mechanism games, suggesting that one cannot safely restrict to one-sided communication mechanisms.