Game theory is an area of mathematics, where patterns and models from entertainment (games), warfare, politics, economics, and probably other disciplines, were found to be common when stripped of distracting and irrelevant details; this is just as mathematics was formed by so stripping applications from numbers and geometry. Just as an Unrestricted Analyst (UA) would master arithmetic, algebra, geometry, and calculus, so a UA should have some game theory in the tool box.
An informal introduction to game theory can spring out of comparing varying games of entertainment, as such games are already abstract models of problems from other disciplines. One might readily jump to the study of probability and statistics (probStat) on exposure to only one variety of game. To analyze the nature of a difference between two varieties of say either poker or bridge or pinocle, one needs to further abstract things to collect the differences into a unifying category.
Game theory is rather unique. The models of games depend on mainstream mathematics, possibly with probStat and formal logic, but game theory also depends on models of players, complete with formulations of goals and “victory conditions” (how an analyst evaluates outcomes). With models of players comes a dependency on information theory, for players in games differ extremely from the actors in chemistry, physics, electronics, cosmology, etc. Players have intentionality, they do not do things just because they are allowed to; players analyze their situations and act in ways they expect will bring them closer to their goal(s).
Essential to analyzing a player is determining what information the player has, especially how the player views the nature of the game and its goals.
I find from the study of game theory that much benefit (and simplification of analyses) seems to come from dividing into two categories all games and all players. Games are either zero-sum or they are not; players have goals that are self-centric or other-centric. Most games we are aware of (ie. entertainment) are zero-sum to a greater or lessor extent, where zero-sum refers to the net impact on some resource by the actions of players; the net impact is zero in that every gain by one player is counterbalanced by a loss to some other player. Very little of life is really zero-sum!
A player with self-centric goals is generally unconcerned by the actions of other players and victory is to end with more than some arbitrary amount (on some scale in the game). [In real life, a self-centric goal might look like accomplishing more than one’s parents did.] A player with other-centric goals is chiefly concerned with accomplishing more than the other players. [In real life, a player with other-centric goals will generally welcome a loss if it is accompanied by greater losses to the other players; a player with such an other-centric perspective will commonly see situations as zero-sum when they are not.]