xxiii Game theory is the name given to the methodology of using mathematical tools to model and analyze situations of interactive decision making... This interactivity distinguishes game theory from standard decision theory... Game theory tries to predict the behavior of the players and sometimes also provides decision makers with suggestions regarding ways in which they can achieve their goals.

p.1 in the game of chess either White (the first mover) has a winning strategy, or Black (the second mover) has a winning strategy, or each player has a strategy guaranteeing at least a draw. This is an important and nontrivial result, especially in view of the fact that to date, it is not known which of the above three alternatives holds, let alone what the winning strategy is, if one exists. [JLJ - perhaps the winning strategy, as demonstrated in correspondence games where a strong player is playing a weaker player, is to create an ultra-stable, resilient position via diagnostic tests of adaptive capacity, and to incrementally improve the position with each small error played by the weaker player. If the weaker player plays no errors, then he was not a weaker player!]

p.9 A game is a mathematical model of a situation of interactive decision making, in which every decision maker (or player) strives to attain his "best possible" outcome, knowing that each of the other players is striving to do the same thing.