Sequential Equilibrium

A refinement of PBE requiring beliefs to be limits of fully mixed strategy perturbations.

Ask the Game theory assistant1 min read · Updated September 9, 2026

Definition

An assessment $(\sigma,\mu)$ is a sequential equilibrium if (i) $\sigma$ is sequentially rational given $\mu$ , and (ii) $\mu$ is consistent: there exist fully mixed $\sigma^n\to\sigma$ with $\mu^n\to\mu$ via Bayes' rule.

Consistency links off-path beliefs to the limit of nearby strategies, ruling out arbitrary belief assignments.

Intuition

Sequential equilibrium demands that beliefs at every information set be the limit of beliefs from small trembles.

It is strictly stronger than PBE but weaker than trembling-hand perfection in the extensive form.

Worked example

Kreps-Wilson (1982) introduced sequential equilibrium to analyze the chain-store paradox and reputation in finitely repeated games.

In signaling games, sequential equilibrium plus the intuitive criterion selects reasonable separating equilibria.

The math

Consistency requires a single sequence of completely mixed behavior strategies converging to $\sigma$ ; $\mu$ is the limit of the induced beliefs.

Kreps-Wilson existence: every finite extensive-form game has a sequential equilibrium.

Where it is used

Reputation models, signaling games, and dynamic games where off-path beliefs matter.

Standard refinement in applied economic theory.

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