The core of game theory is just the min-max result from von Neumann and Morgenstern. Actually, just as mathematics, linear programming is a slightly stronger s

The core of game theory is just the min-max result from von Neumann and Morgenstern. Actually, just as mathematics, linear programming is a slightly stronger subject, and the min-max theorem is a simple consequence of standard results in linear programming. This von Neumann - Morgenstern result is for, say, the game of Paper, Scissors and Rock. Closely related is the J. Nash result on bi-matrix games where, basically, the difference is two payoff matrices instead of just one. Beyond those cases there is the case of games such as chess and checkers. Here it is easy to prove that if players play as best as possible, then the outcome is determined just by who moves first. So, the player who moves first may get always a win, a tie, or a loss, depending on the game. To determine what a player should do, the calculation is a simple tree traversal; the practical problem for games as complicated as chess is that the tree is too big for current computers. As some games illustrate, there can be fast, simple algorithms to determine the moves with no tree traversal at all, but so far apparently no one knows such a simple algorithm for a game such as chess. What else in game theory did you have in mind?