Principal-Agent Problem

A contracting problem where an agent's action is unobservable to the principal.

Ask the Game theory assistant 1 min read · Updated September 9, 2026

Definition

Principal chooses contract $w(y)$ based on observable output $y$ ; agent privately chooses effort $e$ affecting the distribution $F(y\mid e)$ at cost $c(e)$ .

The problem is $\max_{w,e}\mathbb E[y-w(y)]$ s.t.\ IC ( $e\in\arg\max_{e'}\mathbb E u(w)-c(e')$ ) and IR ( $\mathbb E u(w)-c(e)\ge \bar u$ ).

Intuition

Effort must be induced through output-contingent compensation that balances risk-sharing and incentives.

Information asymmetry requires trading off insurance for motivation.

Worked example

CEO compensation via stock options aligns manager and shareholder incentives but imposes risk.

Sharecropping (Stiglitz) splits output to induce effort when labor is unobservable.

The math

Mirrlees-Holmstr\"om first-order approach: $1/u'(w(y))=\lambda+\mu\,\partial\ln f(y\mid e)/\partial e$ (informativeness principle).

Holmstr\"om (1979): any informative signal should be incorporated into the optimal contract.

Where it is used

Executive pay, procurement contracts, insurance, and regulation.

Cornerstone of contract theory.

More in Game theory

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