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Solving nonlinear principal-agent problems using bilevel programming

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  • Cecchini, Mark
  • Ecker, Joseph
  • Kupferschmid, Michael
  • Leitch, Robert

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.

Suggested Citation

  • Cecchini, Mark & Ecker, Joseph & Kupferschmid, Michael & Leitch, Robert, 2013. "Solving nonlinear principal-agent problems using bilevel programming," European Journal of Operational Research, Elsevier, vol. 230(2), pages 364-373.
    • Handle: RePEc:eee:ejores:v:230:y:2013:i:2:p:364-373
    DOI: 10.1016/j.ejor.2013.04.014
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    References listed on IDEAS

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    Cited by:

    1. Singham, D.I., 2019. "Sample average approximation for the continuous type principal-agent problem," European Journal of Operational Research, Elsevier, vol. 275(3), pages 1050-1057.
    2. Kutlu, Levent & Mamatzakis, Emmanuel & Tsionas, Mike G., 2022. "A principal–agent approach for estimating firm efficiency: Revealing bank managerial behavior," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 79(C).
    3. Páez-Pérez, David & Sánchez-Silva, Mauricio, 2016. "A dynamic principal-agent framework for modeling the performance of infrastructure," European Journal of Operational Research, Elsevier, vol. 254(2), pages 576-594.
    4. R. Paulavičius & C. S. Adjiman, 2020. "New bounding schemes and algorithmic options for the Branch-and-Sandwich algorithm," Journal of Global Optimization, Springer, vol. 77(2), pages 197-225, June.
    5. Singham, Dashi I. & Cai, Wenbo & Fügenschuh, Armin, 2021. "Flexible contracting with heterogeneous agents and stochastic demand," International Journal of Production Economics, Elsevier, vol. 231(C).
    6. Sinha, Ankur & Malo, Pekka & Deb, Kalyanmoy, 2017. "Evolutionary algorithm for bilevel optimization using approximations of the lower level optimal solution mapping," European Journal of Operational Research, Elsevier, vol. 257(2), pages 395-411.
    7. Peiyang Su & Ying Peng & Qidan Hu & Ruwen Tan, 2020. "Incentive Mechanism and Subsidy Design for Construction and Demolition Waste Recycling under Information Asymmetry with Reciprocal Behaviors," IJERPH, MDPI, vol. 17(12), pages 1-26, June.
    8. Schosser, Josef, 2019. "Consistency between principal and agent with differing time horizons: Computing incentives under risk," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1113-1123.
    9. Pishchulov, Grigory & Richter, Knut, 2016. "Optimal contract design in the joint economic lot size problem with multi-dimensional asymmetric information," European Journal of Operational Research, Elsevier, vol. 253(3), pages 711-733.

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