Game Theory is the mathematical study of how agents in a system make choices for their actions, in light of the fact that other agents are also making competitive choices of their actions. As the name suggests, the "system" is often some kind of game and the "agents" are players, but game theory is also used to explain the behaviour of crowd motion, business dealings, foreign relations, and even the evolution of altruism. (There's a excellent chapter involving game theory in The Selfish Gene.)
The textbook example of game theory is the Prisoner's Dilemma. The UK game show "Golden Balls" includes a form of the Prisoner's Dilemma where the stake is prizemoney instead of freedom. Each player may independently choose to "split" or "steal" the prize, but if both steal each goes away empty-handed. You might think there aren't many strategic options to guarantee a win in a game like this, but one player found a way:
It's an elegant strategy. Nick is apparently altruistic (or at least risk-averse), and wants to share the prizemoney. But altruistic actions are open to subversion by a selfish opponent. Ibraham, unable to discern Nick's apparent "mutually assured destruction" strategy, has no option but to behave altruistically. I wonder if this strategy has ever been attempted again on the show; but now that this strategy is in the "gene pool" of strategic options, it would likely be less effective the next time around. And that's one of the subtle beauties of Game Theory.
via Business Insider: British Gameshow Contestant Puts On Badass Display Of Game Theory