Pure Strategy

A deterministic choice of an action from a player's strategy set.

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

Definition

A pure strategy for player $i$ is an element $s_i\in S_i$ ; equivalently a degenerate mixed strategy $\sigma_i$ with $\sigma_i(s_i)=1$ .

In extensive-form games, a pure strategy is a complete contingent plan $s_i:H_i\to A$ assigning an action at every information set $h\in H_i$ .

Pure strategies commit to one action without randomization.

They are the building blocks from which mixed strategies are constructed.

In Battle of the Sexes, $(Opera,Opera)$ and $(Football,Football)$ are the two pure Nash equilibria.

Matching Pennies has no pure Nash equilibrium.

A finite game may have zero, one, or many pure Nash equilibria; existence is not guaranteed unlike the mixed case.

In supermodular games with monotone best responses, pure equilibria always exist (Topkis-Milgrom-Roberts).

Frequently used in coordination problems, supply-chain contracting, and engineering design.

Often preferred for interpretability when they exist.

Assembled from the ReLU.chat curated knowledge base. These explanations are concise on purpose; check the sources for anything important.