value of the game

Definition

A two-player game has a value if $\underline{v} = \overline{v}$. The quantity $v := \underline{v} = \overline{v}$ is called the value of the game. Any maxmin and minmax strategies of P1 and P2 respectively are then called optimal strategies.

(convention: P1 maximizer, P2 minimizer)

Notes

The minimax theorem relates when values may be found for mixed strategies.

References

1. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, p. 114.