Martimort, David and Semenov, Aggey and Stole, Lars
(2017):
*A Complete Characterization of Equilibria in a Common Agency Screening Game.*

Preview |
PDF
MPRA_paper_80870.pdf Download (499kB) | Preview |

## Abstract

We characterize the complete set of equilibrium allocations to an intrinsic common agency screening game as the set of solutions to self-generating optimization programs. We provide a complete characterization of equilibrium outcomes for regular environments by relying on techniques developed elsewhere for aggregate games and for the mechanism design delegation literature. The set of equilibria include those with non-differentiable payoffs and discontinuous choices, as well as equilibria that are smooth and continuous in types. We identify one equilibrium, the maximal equilibrium, which is the unique solution to a self-generating optimization program with the largest (or “maximal”) domain, and the only equilibrium that is supported with bi-conjugate (i.e., least-concave) tariffs. The maximal equilibrium exhibits a n-fold distortion caused by each of the n principal’s non-cooperative behavior in over- harvesting the agent’s information rent. Furthermore, in any equilibrium, over any interval of types in which there is full separation, the agent’s equilibrium action corresponds to the allocation in the maximal equilibrium. Under mild conditions, the maximal equilibrium maximizes the agent’s information rent within the class of equilibrium allocations. When the principals’ most-preferred equilibrium allocation differs from the maximal equilibrium, we demonstrate that the agent’s choice function exhibits an interval of bunching over the worst agent types, and elsewhere corresponds with the maximal allocation. The optimal region of bunching trades off the principals’ desire to constrain inefficient n-fold marginalizations of the agent’s rent against the inefficiency of pooling agent types.

Item Type: | MPRA Paper |
---|---|

Original Title: | A Complete Characterization of Equilibria in a Common Agency Screening Game |

Language: | English |

Keywords: | Intrinsic common agency, aggregate games, mechanism design for delegated decision-making, duality, equilibrium selection. |

Subjects: | D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D86 - Economics of Contract: Theory |

Item ID: | 80870 |

Depositing User: | Lars A. Stole |

Date Deposited: | 19 Aug 2017 14:12 |

Last Modified: | 06 Oct 2019 00:51 |

References: | [1] Alonso, N. and R. Matouschek (2008). Optimal Delegation. The Review of Economic Studies, 75: 259-293. [2] Amador, M and K. Bagwell (2013). The Theory of Optimal Delegation with an Application to Tariff Caps. Econometrica, 81: 1541-1599. [3] Bagnoli, C. and T. Bergstrom (2005). Log-Concave Probability and its Ap- plications. Economic Theory, 26: 445-469. [4] Basov, S. (2005). Multi-Dimensional Screening. Springer. [5] Bernheim, D. and M. Whinston (1986a). Common Agency. Econometrica, 54: 923-942. [6] Bernheim, D. and M. Whinston (1986b). Menu Auctions, Resource Allocations and Economic Influence. The Quarterly Journal of Economics, 101: 1-31. [7] Calzolari, G., and V. Denicolo` (2013). Competition with Exclusive Contracts and Market-Share Discounts. The American Economic Review, 103: 2384-2411. [8] Carlier, G. (2001). A General Existence Result for the Principal-Agent Problem with Adverse Selection. Journal of Mathematical Economics, 35: 129-150. [9] Chiesa, G and V. Denicolo` (2009). Trading with a Common Agent under Com- plete Information: A Characterization of Nash Equilibria. Journal of Economic Theory, 144: 296-311. [10] Holmstro ̈m, B. (1984). “On the Theory of Delegation,” Bayesian Models in Economic Theory, eds. M. Boyer and R. Khilstrom, Elsevier Science Publishers. [11] Hoernig, S. and T. Valletti (2011). When Two-Part Tariffs Are Not Enough: Mixing With Nonlinear Pricing. The B.E. Journal of Theoretical Economics 11. [12] Laffont, J.J. and D. Martimort (2002). The Theory of Incentives: The Principal-Agent Model. Princeton University Press. [13] Laffont, J.J. and J. Tirole (1993). A Theory of Incentives in Regulation and Procurement. MIT Press. [14] Laussel, D. and M. LeBreton (1998). Efficient Private Production of Public Goods under Common Agency. Games and Economic Behavior, 25: 194-218. [15] Laussel, D. and M. LeBreton (2001). Conflict and Cooperation: The Structure of Equilibrium Payoffs in Common Agency. Journal of Economic Theory, 100: 93-128. [16] Laussel, D. and J. Resende (2016). Complementary Monopolies with Asymmetric Information. Mimeo Universit ́e Aix-Marseille. [17] Martimort, D. (1992). Multi-Principaux avec Anti-Selection. Annales d’Economie et de Statistiques, 28: 1-38. [18] Martimort, D. (2007). Multi-Contracting Mechanism Design, Advances in Economic Theory Proceedings of the World Congress of the Econometric Society, eds. R. Blundell, A. Newey and T. Persson, Cambridge University Press. [19] Martimort, D. and A. Semenov (2006). Continuity in Mechanism Design without Transfers. Economic Letters, 93 182-189. [20] Martimort, D. and A. Semenov (2008). Ideological Uncertainty and Lobbying Competition. Journal of Public Economics, 92: 456-481. [21] Martimort, D. and L. Stole (2002). The Revelation and Delegation Principles in Common Agency Games. Econometrica, 70: 1659-1674. [22] Martimort, D. and L. Stole (2009a). Market Participation under Delegated and Intrinsic Common Agency Games. The RAND Journal of Economics, 40: 78-102. [23] Martimort, D. and L. Stole (2009b). Selecting Equilibria in Common Agency Games. Journal of Economic Theory, 144: 604-634. [24] Martimort, D. and L. Stole (2012). Representing Equilibrium Aggregates in Aggregate Games with Applications to Common Agency. Games and Economic Behavior, 76: 753-772. [25] Martimort, D. and L. Stole (2015). Menu Auctions and Influence Games with Private Information. Working paper. February 2015. [26] Melumad, N. and T. Shibano (1991). Communication in Settings with no Transfers. The RAND Journal of Economics 22 173-198. [27] Milgrom, P. and I. Segal (2002). Envelope Theorems for Arbitrary Choice Sets. Econometrica, 70: 583-601. [28] Myerson, R. (1982). Optimal Coordination Mechanisms in Generalized Principal-Agent Problems. Journal of Mathematical Economics, 10: 67-81. [29] Peters, M. (2001). Common Agency and the Revelation Principle. Econometrica, 69: 1349-1372. [30] Rochet, J.-C. (1987). A Necessary and Sufficient Condition for Rationalizability in a Quasi-Linear Context. Journal of Mathematical Economics, 16: 191-200. [31] Szentes, B. (2015). Contractible Contracts in Common Agency Problems. The Review of Economic Studies, 82: 391-422. [32] Stole, L. (1991). Mechanism Design under Common Agency. Mimeo University of Chicago. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/80870 |