Game Theory
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Game Theory can be broken down into several categories.
- Linear Programming - Prisoner's Dilemma - Berlekamp Theory (John Conway "Winning Ways for your Mathematical Plays") Surreal numbers - Games of perfect information (go, chess) - Games with perfect information, but a random element (backgammon, monopoly) - Games of imperfect information - Multiple player games (where coalition building is an important part of strategy) (Risk, Poker, voting schemes)
As a minor topic, there are several games from "The Price Is Right" that are mathematically interesting. I remember seeing articles on correct bidding strategy in the "Contestant's row game", and the "Big Wheel game". I remember seeing a good article on correct bidding strategy on "Final Jeopardy"
See also the page on Game theory with a lowercase T.