Abstract
This note establishes that two propositions in the theory of private common agency by Laussel and Le Breton (J. Econ. Theory 100 (2001) 93) extend to a larger class of games, in which each principal's gross monetary payoff does not depend exclusively on the quantities she receives. A new result is offered to demonstrate that Proposition 4.3 is robust to the introduction of negative externalities. An existing result is reinterpreted to show that Proposition 4.2 is robust to the introduction of positive externalities.