Public Contracting in Delegated Agency Games

Martimort, David and Stole, Lars (2011): Public Contracting in Delegated Agency Games.

Abstract

We study games of public delegated common agency under asymmetric information. Us- ing tools from non-smooth analysis and optimal control, we derive best responses and characterize equilibria (both continuous and discontinuous) using self-generating opti- mization programs of which any equilibrium allocation must be a solution. Special atten- tion is given to common agency games in which each principal’s payoff is a linear function of the agent’s action. In such games the self-generating optimization program reduces to the maximization of the principals’ “aggregate” virtual surplus in which the agent’s marginal valuation is replaced by a confluence of “virtual” valuations that reflect com- mon agency problems. One noteworthy subset of equilibrium allocations are “virtually truthful” which are the incomplete-information generalization of Bernheim and Whin- ston’s (1986) “truthful” equilibria. Virtually-truthful equilibria are simple to calculate and illustrate two distinct sources of equilibrium distortion: inefficient contracting by a given coalition of active principals and inefficient participation (insufficient activity) by principals. Our results are illustrated by means of two games: a public goods game in which each player simultaneously offers a menu contract to a common provider of the public good in order to induce greater supply, and a lobbying game between conflicting interest groups in which each group offers a menu of contributions to a common political decision-maker in an attempt to influence policymaking.

• Item Type: MPRA Paper
• Language: English
• Keywords: Common agency, asymmetric information, menu auctions, delegated contracting games, public goods, lobbying, non-smooth analysis, non-smooth control
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D73 - Bureaucracy ; Administrative Processes in Public Organizations ; Corruption; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Aliprantis, C. and K. Border (1990). Infinite Dimensional Analysis, 2nd ed. Berlin: Springer.

Alonso, N. and R. Matouschek (2008). Optimal Delegation. Review of Economic Studies 75 259–293.

Bagnoli, C. and T. Bergstrom (2005). Log-Concave Probability and its Applications. Economic Theory 26 445–469.

Bergstrom, T., L. Blume and H. Varian (1986). On the Private Provision of Public Goods. Journal of Public Economics 29 25–49.

Bernheim, D. and M. Whinston (1986a). Menu Auctions, Resource Allocations and Economic Influence. Quarterly Journal of Economics 101 1–31.

Bernheim, D. and M. Whinston (1986b). Common Agency. Econometrica 54 923–942.

Bernheim, D. and M. Whinston (1998). Exclusive Dealing. Journal of Political Economy 106, 64–103.


Biais, B., D. Martimort and J.C. Rochet (2000). Competing Mechanisms in a Common Value Environment. Econometrica 68 799–837.


Calzolari, G. and V. De Nicolo (2010). Competition With Exclusive Contracts and Market-Share Discounts. CEPR Discussion Paper 7613.

Calzolari, G. and C. Scarpa (2008). Delegated and Intrinsic Common Agency with Full Mar- ket Participation. Unpublished manuscript, University of Bologna.

Champsaur, P. and J.C. Rochet (1989). Multiproduct Duopolists. Econometrica 57 533–557.

Chiesa, G. and V. Denicolo (2009). Trading with a Common Agent under Complete Information: A Characterization of Nash Equilibria. Journal of Economic Theory 144 296–311.

Clarke, F. (1990). Optimization and Nonsmooth Analysis. Philadelphia: SIAM.

Dixit, A., G. Grossman and E. Helpman (1997). Common Agency and Coordination: General Theory and an Application to Government Decision-Making. Journal of Political Economy 105 752–769.

Galbraith, G and R. Vinter (2004). Regularity of Optimal Controls for State-Constrained Problems. Journal of Global Optimization 28 305–317.

Grossman, G. and E. Helpman (1994). Protection for Sale. American Economic Review 84 833–850.

Hoernig, S. and T. Valletti (2010). When Two-Part Tariffs Are Not Enough: Mixing With Nonlinear Pricing. Unpublished manuscript, CEPR Discussion Paper 7720.

Holmstro ̈m, B. (1984). On the Theory of Delegation, in Bayesian Models in Economic Theory, ed. by M. Boyer and R. Kihlstrom, Elsevier Science B. V.

Innes, R., (1990). Limited liability and incentive contracting with ex-ante action choices,” Journal of Economic Theory 52 47–65.

Ivaldi, M. and D. Martimort (1994). Competition under Nonlinear Pricing. Annales d’Economie et de Statistique 34 71–114.

Jullien, B. (2000). Participation Constraints in Adverse Selection Models. Journal of Economic Theory 93 1–47.

Laffont, J.J. and D. Martimort (2002). The Theory of Incentives: The principal-Agent Model. Princeton: Princeton University Press.

Laussel, D. and M. Lebreton (1998). Efficient Private Production of Public Goods under Common Agency. Games and Economic Behavior 25 194–218.

Laussel, D. and M. Lebreton (2001). Conflict and Cooperation: The Structure of Equilibrium Payoffs in Common Agency. Journal of Economic Theory 100 93–128.

Lebreton, M. and F. Salanie ́ (2003). Lobbying under Political Uncertainty. Journal of Public Economics 87 2589–2610.

Lewis, T. and D. Sappington (1989). Countervailing Incentives in Agency Problems. Journal of Economic Theory 49 294–313.

Loewen, P. and T. Rockafellar (1995). New Necessary Conditions for the Generalized Bolza Problem. SIAM Journal of Control and Oprimization 49 294–313.

Maggi, G. and A. Rodriguez-Clare (1995). On Countervailing Incentives. Journal of Economic Theory 66 238–263.

Martimort, D. (1992). Multi-Principaux avec Anti-Selection. Annales d’Economie et de Statis- tiques 28 1–38.

Martimort, D. (1996). The Multi-principal Nature of Government. European Economic Review 40 673–685.

Martimort, D. (2007). Multicontracting Mechanism Design. Advances in Economic Theory, Proceedings of the 2005 World Congress of the Econometric Society, ed. by R. Blundell, W. Newey and T. Person. Cambridge: Cambridge University Press.

Martimort, D. and A. Semenov (2006). Continuity in Mechanism Design without Transfers. Economic Letters, 93 182–189.

Martimort, D. and A. Semenov (2008). Ideological Uncertainty and Lobbying Competition. Journal of Public Economics 92 456–481.

Martimort, D. and L. Stole (2002). The Revelation and Delegation Principles in Common Agency Games. Econometrica 70 1659–1674.

Martimort, D. and L. Stole (2003). Contractual Externalities and Common Agency Equilib- ria. Advances in Theoretical Economics 3(1), Article 4, http://www.bepress.com/bejte.

Martimort, D. and L. Stole (2009a). Market Participation in Delegated and Intrinsic Common Agency Games. RAND Journal of Economics 40 78–102.

Martimort, D. and L. Stole (2009b). Selecting Equilibria in Common Agency Games. Jour- nal of Economic Theory 144 604–634.

Martimort, D. and L. Stole (2011). Aggregate Representations of Aggregate Games with Applications to Common Agency Games. Unpublished manuscript, University of Chicago.

Melumad, N. and T. Shibano (1991). Communication in Settings with no Transfers. RAND Journal of Economics 22 173–198.

Mezzetti, C. (1997). Common Agency with Horizontally Differentiated principals. RAND Journal of Economics 28 323–345.

Milgrom, P. and I. Segal (2002). Envelope Theorems for Arbitrary Choice Sets. Econometrica 70 583–601.

Peters, M. and B. Szentes (2011). Definable and Contractible Contracts. Unpublished manuscript, University College of London, forthcoming Econometrica.

Rochet, J.C. and L. Stole (2002). Nonlinear Pricing with Random Participation. Review of Economic Studies 69 277–311.

Rockafellar, T. and R. Wets (2004). Variational Analysis. Berlin: Springer. Royden, H.L. (1988). Real Analysis. New York: Prentice Hall.

Seierstad, A. and K. Sydsaeter (1987). Optimal Control Theory with Economic Applications. Amsterdam: North Holland.

Stole, L. (1991). Mechanism Design under Common Agency. Unpublished manuscript, University of Chicago.

Stole, L. (1995). Nonlinear Pricing and Oligopoly. Journal of Economics and Management Strategy 4 529–562.

Stole, L. (2007). Price Discrimination in Competitive Environments. Handbook of Industrial Organization, Volume 3, ed. by Armstrong, M. and Porter, R. Amsterdam: North Holland, 2221– 2299.

Vinter, R. (2000). Optimal Control. Boston: Birkhauser.


Vinter, R. and H. Zheng (1995). Necessary Conditions for Optimal Control Problem with State Constraints. Transactions of the American Mathematical Society 350 1181–1204.