Game theory:- value of a game? I haven't found any suitable explanation or even definition for this concept. What is the value of game in game theory? Can anybody explain it to me with an example.
 A: The value of a game is the expected value to a given player.  For example, a game where you flip a coin and win $2$ for heads and lose $1$ for tails has a value to you of $\frac 12\cdot 2 + \frac 12 \cdot (-1)=\frac 12$.  If you have to pay $\frac 12$ to play the game you will break even in the long run.
A: One definition of the "value of a game" is as the nim-value or "nimber" of a game. The Sprague-Grundy Theorem says that all games (satisfying a few standard assumptions true of most combinatorial games) are equivalent to a single nimheap, i.e. they behave the same way under game addition. The number of stones in the nimheap is the "nimber," which is perhaps what the value of a game means.
More reading:
https://en.wikipedia.org/wiki/Nimber
https://mathworld.wolfram.com/Nim-Value.html
https://en.wikipedia.org/wiki/Sprague–Grundy_theorem
A: As in general game theory, the Value of game is to be the minimax of the payoff. Symbolically,
$$V(x)=\min_{\phi(x)}\max_{\psi(x)}(\text{ payoff }).$$
From Rufus Isaacs - Differential Games_ A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization
