Common Agency Equilibria with Discrete Mechanisms and Discrete Types

This paper characterizes the equilibrium sets of an intrinsic common agency game with discrete types and direct revelation mechanisms. After presenting a general algorithm to find the pure-strategy equilibria of this game, we use it to characterize these equilibria when the two principals control activities which are complements in the agent’s objective function. Some of those equilibria may entail allocative inefficiency. For the case of substitutes, we demonstrate non-existence of such equilibria with direct mechanisms, but existence may be obtained with indirect mechanisms. Finally, we relax the equilibrium concept and analyze quasi-equilibria. We show that existence is then guaranteed and characterize the corresponding allocations.