This paper considers common agency games with non-quasilinear payoff functions. The main purpose is to extend the research on the rent of the agent at the truthful equilibria by Laussel and Le Breton (2001). We give the sufficient conditions under which the agent obtains no rent at any truthful equilibrium and the agent obtains positive rent at any truthful equilibrium. These sufficient conditions are stated in terms of the NTU coalitional game derived from a common agency game. The former has a similar form with the NTU ordinary convexity, and the latter is stated as an application of the reduced game. We also show the equivalence of the strictly strong equilibrium and the truthful equilibrium with no rent. Further, we consider some applications.

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