Negotiation and take-it or leave-it in common agency with non-contractible actions

In a recent paper, Peters [Negotiation and take-it or leave-it in common agency, J. Econ. Theory 111 (2003) 189–228] identifies a set of restrictions on players’ preferences, called “no-externalities assumption”, under which, in common agency games, there is no loss of generality in restricting principals’ strategies to be take-it or leave-it offers. The present note provides an example to show that these conditions are not sufficient when the agent takes a non-contractible action.