A folk theorem for competing mechanisms

We provide a partial characterization of the set of outcome functions that can be supported as perfect Bayesian equilibrium in the recommendation game described in [T. Yamashita, Mechanism games with multiple principals and three or more agents, Econometrica 78 (2) (2010) 791-801]. We show that the set of outcome functions that can be supported is at least as large as the set supportable by a mechanism designer in the sense of Myerson (Myerson, 1979 [13]). We show how to support random and correlated outcomes as equilibrium outcomes in the recommendation game.