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A Complete Characterization of Equilibria in Two-type Common Agency Screening Games

Martimort, David and Semenov, Aggey and Stole, Lars (2015): A Complete Characterization of Equilibria in Two-type Common Agency Screening Games.

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We characterize the complete set of equilibrium allocations to a two-type intrinsic common agency screening game as the set of solutions to a self-generating optimization program. The program, in turn, can be thought of as a maximization problem facing a fictional “surrogate” principal with a simple set of incentive constraints that embed the non-cooperative behavior of principals in the underlying game. After providing a complete characterization of equilibrium outcomes, we refine the set by imposing a requirement of biconjugacy on equilibrium tariffs: In biconjugate equilibria, the surrogate principal’s incentive constraints are described by marginal conditions. Biconjugate equilibria always exist, they are simple to compute, and they are robust in the sense that they remain equilibria when “out-of-equilibrium” output-price pairs are pruned. After characterizing the set of biconjugate equilibrium allocations, we ask what is the best equilibrium for the principals from an ex ante perspective. We show that the allocation that maximizes the principals’ ex ante collective payoff among all possible equilibria is distinct from the best allocation in the refined set of biconjugate equilibria, although their qualitative properties remain similar.

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