completely mixed strategy

Definition

A mixed strategy $\sigma_i$ of player $i$ is called completely mixed if $\sigma_i(s_i) > 0$ for each $s_i \in S_i$. A behavior strategy $\sigma_i$ of player $i$ is called completely mixed if $\sigma_i(U_i; a_i) > 0$ for each information set $U_i$ of player $i$, and each action $a_i \in A(U_i)$.

Corollary

Let $\Gamma$ be an extensive form game. Then every Nash equilibrium in completely mixed strategies (behavior strategies or mixed strategies) is a subgame perfect equilibrium.

See also

• equivalent mixed and behavior strategies

References

1. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, p. 256.