Contractual Externalities and Common Agency Equilibria

This paper characterizes the equilibrium sets of common agency games with direct externalities between principals when they compete with nonlinear prices. Direct externalities arise when the contracting variable of one principal directly affects the other principal's payoff. First, we characterize the set of pure-strategy, symmetric equilibria under complete information of an intrinsic common agency game. This set of equilibria is large because of the presence of price-output offers by the principals that are unchosen by the agent in equilibrium. Equilibria exist in which principals offer out-of-equilibrium price-output choices to the agent and induce aggressive, low-price behavior corresponding to marginal-cost pricing in the extreme case. We then show that this equilibrium set of outputs is robust to the possibility that agent refuses any of the offered contracts; the case of delegated agency. Second, we introduce asymmetric information in order to rationalize existing nonlinear pricing contracts. The introduction of asymmetric information has the effect of restricting the set of equilibrium outputs of the intrinsic common agency game.