Solving nonlinear principal-agent problems using bilevel programming

Mark Cecchini, Joseph Ecker, Michael Kupferschmid and Robert Leitch

European Journal of Operational Research, 2013, vol. 230, issue 2, 364-373

Abstract: While significant progress has been made, analytic research on principal-agent problems that seek closed-form solutions faces limitations due to tractability issues that arise because of the mathematical complexity of the problem. The principal must maximize expected utility subject to the agent’s participation and incentive compatibility constraints. Linearity of performance measures is often assumed and the Linear, Exponential, Normal (LEN) model is often used to deal with this complexity. These assumptions may be too restrictive for researchers to explore the variety of relationships between compensation contracts offered by the principal and the effort of the agent. In this paper we show how to numerically solve principal-agent problems with nonlinear contracts. In our procedure, we deal directly with the agent’s incentive compatibility constraint. We illustrate our solution procedure with numerical examples and use optimization methods to make the problem tractable without using the simplifying assumptions of a LEN model. We also show that using linear contracts to approximate nonlinear contracts leads to solutions that are far from the optimal solutions obtained using nonlinear contracts. A principal-agent problem is a special instance of a bilevel nonlinear programming problem. We show how to solve principal-agent problems by solving bilevel programming problems using the ellipsoid algorithm. The approach we present can give researchers new insights into the relationships between nonlinear compensation schemes and employee effort.

Keywords: Agency theory; Compensation contracts; Performance measures; Nonlinear optimization; Principal-agent problems; Bilevel nonlinear programming (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:230:y:2013:i:2:p:364-373

DOI: 10.1016/j.ejor.2013.04.014

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