minimax theorem

Theorem

In any Matrix game $A$, the average security levels of the players in mixed strategies coincide, that is, $$\overline{V}_m(A) = \min_Y \max_Z y' Az = \max_Z \min_Y y' Az = \underline{V}_m(A)$$

Corollary

#incomplete

References

1. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, pp. 27-28.