principal-agent model

Overview

• principal-agent model: a principal interacts with an agent
• agent: set of actions $\mathcal{A}$ of size $n$
  • action costs for agent: $0 \leq c_1 \leq ... \leq c_n$
• agent's technology: probability matrix $\mathbf{q} = \{q_{ij}\}_{i \in [n],j \in [m]}$ describing stochastic outcome from agent's action
  • $q_{ij}$ probability of outcome $j$ under action $i$
  • $i$th row $\mathbf{q}_i$ is distribution (probability mass function) over rewards induced from action $i$
• expected welfare from action $i$:
• contract: payment rule $\mathbf{t} = (t_1,...,t_m)$ of different transfers for each of the $m$ outcomes
• solving principal-agent problem: designing contract $\mathbf{t}$

Notes

• in algorithmic contract theory
• considerations: expected payment by agent, agent's best response, principal's expected utility from contract, incentive compatibility and individual rationality
• variants such as combinatorial contracts, etc

References

1. B. Holmström, “Moral Hazard and Observability,” The Bell Journal of Economics, vol. 10, no. 1, pp. 74–91, 1979, doi: 10.2307/3003320.
2. S. J. Grossman and O. D. Hart, “An Analysis of the Principal-Agent Problem,” in Huebner International Series on Risk, Insurance and Economic Security, Dordrecht: Springer Netherlands, 1992, pp. 302–340. doi: 10.1007/978-94-015-7957-5_16.
3. P. Duetting, M. Feldman, and I. Talgam-Cohen, “Algorithmic Contract Theory: A Survey,” Dec. 20, 2024, arXiv: arXiv:2412.16384. doi: 10.48550/arXiv.2412.16384.
4. P. Duetting, T. Ezra, M. Feldman, and T. Kesselheim, “Combinatorial Contracts,” Sep. 02, 2025, arXiv: arXiv:2109.14260. doi: 10.48550/arXiv.2109.14260.
5. Y. Chen, Z. Chen, X. Deng, and Z. Huang, “Are Bounded Contracts Learnable and Approximately Optimal?,” Feb. 22, 2024, arXiv: arXiv:2402.14486. doi: 10.48550/arXiv.2402.14486.