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Approximating combinatorial contracts with a cardinality constraint

Author

Listed:
  • Qinqin Gong

    (Beijing University of Technology)

  • Ling Gai

    (University of Shanghai for Science and Technology)

  • Yanjun Jiang

    (Ludong University)

  • Yang Lv

    (Beijing University of Technology)

  • Ruiqi Yang

    (Beijing University of Technology)

Abstract

We explore the problem of combinatorial contract design, a subject introduced and studied by Dütting et al. (2023). Previous research has focused on the challenge of selecting an unconstrained subset of agents, particularly when the principal’s utility function exhibits XOS or submodular characteristics related to the subset of agents that exert effort. Our study extends this existing line of research by examining scenarios in which the principal aims to select a subset of agents with a specific k-cardinality constraint. In these scenarios, the actions that each agent can take are binary values: effort or no effort. We focus on linear contracts, where the expected reward function is XOS or submodular. Our contribution is an approximation of 0.0197 for the problem of designing multi-agent hidden-action principal-agent contracts with the k-cardinality constraint. This result stands in contrast to the unconstrained setting, where Dütting et al. (2023) achieved an approximation of nearly 0.0039.

Suggested Citation

  • Qinqin Gong & Ling Gai & Yanjun Jiang & Yang Lv & Ruiqi Yang, 2025. "Approximating combinatorial contracts with a cardinality constraint," Journal of Combinatorial Optimization, Springer, vol. 49(5), pages 1-16, July.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:5:d:10.1007_s10878-025-01307-1
    DOI: 10.1007/s10878-025-01307-1
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