We consider a class of mechanism games in which there are multiple principals and three or more agents. For a mechanism game in this class, a sort of folk theorem holds: there is a threshold value for each of the principals such that an allocation is achieved at a pure‐strategy sequential equilibrium of the game if and only if (i) it is incentive compatible and (ii) it attains an expected utility for each principal that is greater than or equal to the threshold value for the principal.