Bounds on the Welfare Loss from Moral Hazard with Limited Liability

We study a principal–agent problem with discrete outcome and effort level spaces. The principal and the agent are risk neutral and the latter is subject to limited liability. Quantifying welfare loss as the ratio between the first-best social welfare and that arising from the principal's optimal pay-for-performance contract, we provide simple parametric bounds for problem instances with moral hazard. Relying on that, we compute the worst-case welfare loss ratio among all problem instances with a fixed number of effort and outcome levels as a function of the number of possible effort levels and the likelihood ratio evaluated at the highest outcome. As extensions, we look at linear contracts and at cases with multiple identical tasks. Our work constitutes an initial attempt to quantify the losses arising from moral hazard when the agent is subject to limited liability, and shows that these losses are non-negligible in the worst case.

[1]  R. Innes.  Limited liability and incentive contracting with ex-ante action choices , 1990 .

[2]  J. Mirrlees.  The Theory of Moral Hazard and Unobservable Behaviour: Part I , 1999 .

[3]  James A. Mirrlees,et al.  Notes on Welfare Economics, Information, and Uncertainty , 2006 .

[4]  C. Shapiro,et al.  Equilibrium Unemployment as a Worker Discipline Device , 1984 .

[5]  Paul R. Milgrom,et al.  Multitask Principal–Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design , 1991 .

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

[7]  K. Brown,et al.  Of Tournaments and Temptations: An Analysis of Managerial Incentives in the Mutual Fund Industry , 1996 .

[8]  Hervé Moulin,et al.  Almost budget-balanced VCG mechanisms to assign multiple objects , 2009, J. Econ. Theory.

[9]  Son Ku Kim,et al.  Efficiency of an Information System in an Agency Model , 1995 .

[10]  Bernard Salanié.  Testing Contract Theory , 2003 .

[11]  Joseph E. Stiglitz,et al.  Incentives and Risk Sharing in Sharecropping , 1974 .

[12]  Paul Oyer,et al.  Fiscal Year Ends and Nonlinear Incentive Contracts: The Effect on Business Seasonality , 1998 .

[13]  Bengt Holmstrom,et al.  Moral Hazard and Observability , 1979 .

[14]  Asuman E. Ozdaglar,et al.  Price and Capacity Competition , 2006, Games Econ. Behav..

[15]  Glenn Ellison,et al.  Career Concerns of Mutual Fund Managers , 1998 .

[16]  José R. Correa,et al.  A Geometric Approach to the Price of Anarchy in Nonatomic Congestion Games , 2008, Games Econ. Behav..

[17]  Carl Shapiro,et al.  Equilibrium Unemployment as a Worker Discipline Device: Reply , 1985 .

[18]  Christian Laux,et al.  Limited Liability and Incentive Contracting with Multiple Projects , 2001 .

[19]  Frank Kelly,et al.  Charging and rate control for elastic traffic , 1997, Eur. Trans. Telecommun..

[20]  John R. Conlon,et al.  TWO NEW CONDITIONS SUPPORTING THE FIRST-ORDER APPROACH TO MULTISIGNAL PRINCIPAL-AGENT PROBLEMS , 2009 .

[21]  R. Zeckhauser,et al.  Insurance, Information, and Individual Action , 1971 .

[22]  Christos H. Papadimitriou,et al.  Worst-case equilibria , 1999 .

[23]  John N. Tsitsiklis,et al.  Efficiency loss in a network resource allocation game: the case of elastic supply , 2005, IEEE Trans. Autom. Control..

[24]  Paul R. Milgrom,et al.  AGGREGATION AND LINEARITY IN THE PROVISION OF INTERTEMPORAL INCENTIVES , 1987 .

[25]  Moshe Babaioff,et al.  Free-Riding and Free-Labor in Combinatorial Agency , 2009, SAGT.

[26]  Tim Roughgarden,et al.  Algorithmic Game Theory , 2007 .

[27]  David L. Wallace,et al.  A Convolutive Class of Monotone Likelihood Ratio Families , 1959 .

[28]  William P. Rogerson,et al.  THE FIRST-ORDER APPROACH TO PRINCIPAL-AGENT PROBLEMS , 1985 .

[29]  Steven A. Matthews.  Renegotiating Moral Hazard Contracts under Limited Liability and Monotonicity , 2001, J. Econ. Theory.

[30]  Daniel F. Spulber,et al.  The Form of Incentive Contracts: Agency with Moral Hazard, Risk Neutrality and Limited Liability , 2012 .

[31]  Son Ku Kim,et al.  Limited Liability and Bonus Contracts , 1997 .

[32]  J. Mirrlees.  The Optimal Structure of Incentives and Authority Within an Organization , 1976 .

[33]  M. Rothschild,et al.  Increasing risk: I. A definition , 1970 .

[34]  Ian Jewitt,et al.  Justifying the First-Order Approach to Principal-Agent Problems , 1988 .

[35]  Sanford J. Grossman,et al.  AN ANALYSIS OF THE PRINCIPAL-AGENT PROBLEM , 1983 .

[36]  H. Moulin.  The price of anarchy of serial, average and incremental cost sharing , 2008 .

[37]  Beth J. Asch.  Do Incentives Matter? The Case of Navy Recruiters , 1990 .

[38]  J. Tirole,et al.  Financial Intermediation, Loanable Funds, and The Real Sector , 1997 .

[39]  Felipe Balmaceda,et al.  Optimal Task Assignments , 2016, Games Econ. Behav..

[40]  M. C. Jensen,et al.  Production Functions : An Application to Labor-Managed Firms and Codetermination , 2015 .

[41]  Tim Roughgarden,et al.  Bounding the inefficiency of equilibria in nonatomic congestion games , 2004, Games Econ. Behav..

[42]  Moshe Babaioff,et al.  Combinatorial agency , 2006, ACM Conference on Economics and Computation.

[43]  Claude Fluet,et al.  Mechanism Sufficient Statistic in the Risk-Neutral Agency Problem , 1998 .

[44]  José R. Correa,et al.  Decision , Risk and Operations Working Papers Series The cost of moral hazard and limited liability in the principal-agent problem , 2010 .

[45]  P. Healy.  The effects of bonus schemes on accounting decisions , 2015 .

[46]  Philip A. Neher,et al.  Peasants, Procreation, and Pensions , 1971 .

[47]  Huynh Huynh,et al.  A new proof for monotone likelihood ratio for the sum of independent bernoulli random variables , 1994 .

[48]  H. Demsetz,et al.  Production, Information Costs, and Economic Organization , 1975, IEEE Engineering Management Review.