Optimal delegation with multi-dimensional decisions

This paper investigates optimal mechanisms in a principal–agent framework with a two-dimensional decision space, quadratic payoffs and no monetary transfers. If the conflicts of interest between the principal and the agent are different on each dimension, then delegation is always strictly valuable. The principal can better extract information from the agent by using the spread between the two decisions as a costly screening device. Delegation sets no longer trade off pooling intervals and intervals of full discretion but instead take more complex shapes. We use advanced results from the calculus of variations to ensure existence of a solution and derive sufficient and necessary conditions for optimality. The optimal mechanism is continuous and deterministic. The agentʼs informational rent, the average decision and its spread are strictly monotonic in the agentʼs type. The comparison of the optimal mechanism with standard one-dimensional mechanisms shows how cooperation between different principals controlling various dimensions of the agentʼs activities facilitates information revelation.

[1]  Bengt Holmstrom,et al.  On The Theory of Delegation , 1980 .

[2]  Roger G. Noll,et al.  Administrative Procedures as Instruments of Political Control , 1987 .

[3]  R. Gibbons,et al.  Cheap Talk with Two Audiences , 1989 .

[4]  M. Battaglini.  Policy Advice with Imperfectly Informed Experts , 2004 .

[5]  M. Armstrong.  Multiproduct Nonlinear Pricing , 1996 .

[6]  J. Sobel,et al.  STRATEGIC INFORMATION TRANSMISSION , 1982 .

[7]  B. Holmström,et al.  On incentives and control in organizations , 1977 .

[8]  Tracy R. Lewis,et al.  Inflexible Rules in Incentive Problems , 1989 .

[9]  D. Martimort,et al.  The Informational Effects of Competition and Collusion in Legislative Politics , 2008 .

[10]  Tracy R. Lewis,et al.  Countervailing incentives in agency problems , 1989 .

[11]  Paul R. Milgrom,et al.  Envelope Theorems for Arbitrary Choice Sets , 2002 .

[12]  David P. Baron,et al.  Legislative Organization with Informational Committees , 2000 .

[13]  Tymofiy Mylovanov,et al.  Stochastic mechanisms in settings without monetary transfers: The regular case , 2009, J. Econ. Theory.

[14]  D. Martimort,et al.  Multidimensional communication mechanisms: cooperative and conflicting designs , 2008 .

[15]  Daniel J. Seidmann,et al.  Optimal Delegation with a Finite Number of States , 2011 .

[16]  Wouter Dessein,et al.  When Does Coordination Require Centralization? , 2006 .

[17]  J. Mirrlees.  An Exploration in the Theory of Optimum Income Taxation an Exploration in the Theory of Optimum Income Taxation L Y 2 , 2022 .

[18]  D. Szalay,et al.  Optimal Delegation , 2022 .

[19]  Marco Battaglini,et al.  Multiple Referrals and Multidimensional Cheap Talk , 2002 .

[20]  Luciano Messori.  The Theory of Incentives I: The Principal-Agent Model , 2013 .

[21]  Gregory Pavlov,et al.  How to talk to multiple audiences , 2011, Games Econ. Behav..

[22]  A. Ambrus,et al.  Multi-sender cheap talk with restricted state spaces , 2008 .

[23]  Nahum D. Melumad,et al.  Communication in settings with no transfers , 1991 .

[24]  H. Fang,et al.  Optimal Provision of Multiple Excludable Public Goods , 2006 .

[25]  S. Athey,et al.  THE OPTIMAL DEGREE OF DISCRETION IN MONETARY POLICY BY SUSAN ATHEY, , 2005 .

[26]  Gilat Levy,et al.  On the Limits of Communication in Multidimensional Cheap Talk: A Comment , 2004 .

[27]  J. Morgan,et al.  A Model of Expertise , 1999 .

[28]  David Martimort,et al.  Advances in Economics and Econometrics: Multi-Contracting Mechanism Design , 2006 .

[29]  Artur Raviv,et al.  The Capital Budgeting Process: Incentives and Information , 1996 .

[30]  John D. Huber,et al.  Politics, Delegation, and Bureaucracy , 2008 .

[31]  Niko Matouschek,et al.  Relational Delegation , 2005, SSRN Electronic Journal.

[32]  Barry R. Weingast,et al.  The Oxford Handbook of Political Economy , 2006 .

[33]  D. Austen-Smith.  Interested Experts and Policy Advice: Multiple Referrals under Open Rule , 1993 .

[34]  G. Huber.  Deliberate Discretion? The Institutional Foundations of Bureaucratic Autonomy. By John D. Huber and Charles R. Shipan. New York: Cambridge University Press, 2002. 304p. $65.00 cloth, $24.00 paper , 2004, Perspectives on Politics.

[35]  R. Myerson.  Optimal coordination mechanisms in generalized principal–agent problems , 1982 .

[36]  J. Rochet,et al.  Ironing, Sweeping, and Multidimensional Screening , 1998 .

[37]  Wouter Dessein.  Authority and Communication in Organizations , 2002 .

[38]  Francesco Giovannoni,et al.  Deliberate Discretion?: The Institutional Foundations of Bureaucratic Autonomy. , 2004 .

[39]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[40]  Mark Armstrong,et al.  Delegation and discretion , 1994 .

[41]  J. Laffont,et al.  The Theory of Incentives: The Principal-Agent Model , 2001 .

[42]  J. Rochet.  The taxation principle and multi-time Hamilton-Jacobi equations☆ , 1985 .

[43]  Richard Arnott,et al.  Randomization with Asymmetric Information , 1988 .

[44]  Archishman Chakraborty,et al.  Comparative Cheap Talk , 2005, J. Econ. Theory.

[45]  Archishman Chakraborty,et al.  Comparative Cheap Talk , 2005 .

[46]  Monotonicity in Direct Revelation Mechanisms , 2003 .

[47]  Thomas W. Gilligan,et al.  Collective Decisionmaking and Standing Committees: An Informational Rationale for Restrictive Amendment Procedures , 1987 .

[48]  Navin Kartik,et al.  Pandering to Persuade , 2010 .

[49]  Gregory Pavlov,et al.  Mediation, arbitration and negotiation , 2009, J. Econ. Theory.

[50]  D. Martimort,et al.  Continuity in Mechanism Design without Transfers , 2006 .