Common Agency Games with Common Value Exclusion, Convexity and Existence

We consider the model common agency proposed by Biais Martimort and Ro- chet (2000, 2013). We show that in this setting there is no symmetric equilibrium as the one characterized in those articles. We argue that the equilibrium price sched- ules cannot be simultaneously convex and concave. In particular in the monopoly case, under some classical assumptions, some agents will be excluded from trade. In the other that a price schedule at any symmetric equilibrium must be must be convex and concave. We conclude that a symmetric equilibrium cannot exist and discuss the implications of our result and the links with the existing literature.