Upper and Lower Value of a two person zero sum game

Question

I understand that if a game's lower value V$_{L}$ is equal to it's upper value V$_{U}$ then the game has a value V$=$V$_{U}$=V$_L$. Just to be sure it is also the case that if a game has a value V then V$=$V$_{U}$=V$_L$, by definition?

Answer 1

Yes. The game has a value if and only its lower value equals its upper value, and that common value is the value of the game. It follows that if the game has a value, then that value is also its lower and upper value. See also the definition on page II-37 in these notes.