mixed strategy

Definition

A mixed strategy for a player is a probability distribution on the space of his pure strategies. Equivalently, a random variable whose values are the player's pure strategies.

Define

• $\Sigma_i$, player $i$'s set of mixed strategies
• $\mathcal{B}_i$, player $i$'s set of behavior strategies

Mixed/behavior strategy vector

see mixed/behavior strategy vector

Equivalent mixed and behavior strategies

See equivalent mixed and behavior strategies

Computation of mixed equilibrium strategies

#incomplete

Theorem (convexity and compactness of mixed strategies for finite pure strategy set)

If player $i$'s set of pure strategies $S_i$ is finite, then his set of mixed strategies $\Sigma_i$ is convex and compact.

References

1. T. Başar and G.J. Olsder, Dynamic Noncooperative Game Theory, 2nd edition, Classics in Applied Mathematics, SIAM, Philadelphia, 1999, pp. 23-29.
2. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, pp. 222-223
3. https://knowledgehive.github.io/Game-Theory/lecture 9.html