Contractual Externalities and Common Agency Equilibria

This paper characterizes the equilibrium sets of an intrinsic common agency game with direct externalities between principals both under complete and asymmetric information. Direct externalities arise when the contracting variable of one principal affects directly the other principal's payoff. Out-of-equilibrium messages are used by principals to precommit themselves to distort their strategic behavior. We characterize pure-strategy symmetric equilibria arising in such games under complete information and show their multiplicity. We then introduce asymmetric information to refine the set of feasible conjectures. We show that a unique equilibrium may be selected by conveniently perturbing the information structure. Both under complete and asymmetric information, we show that the equilibrium outputs of the intrinsic common agency game are also equilibrium outputs of the delegated common agency game, although the two games differ in terms of the distribution of surplus they involve