In this note we argue that in Common Agency games, the restriction to deterministic menus is crutial.We give an simple example (complete information, no moral hazard) in which an equilibrium is not robust to the introduction of stochastic menus.

In common agency games, one cannot characterize all equilibria by considering only direct mechanisms. In an attempt to overcome this difficulty, Peters [Econometrica, 2001] and Martimort and Stole [Econometrica, 2002] identified a class of indirect mechanisms (namely, menus) which are able to...