Introduction to Game Theory/Strategic games

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Like most sciences, Game theory is an attempt to model the world in a way we can understand. The simplest way game theorists can model the world is in a strategic game. Strategic games have three components: a set of players, for each player a set of strategies, and a preference over all strategies. The players in the game are exactly the players in the strategic model. Each player also needs a set of strategies, or what moves to take during the course of the game. By giving each player a strategy, we get the outcome of the game. Each player needs a preference for every possible outcome. In mathematical notation:

Players: $\{1,2,\dots N\}$

Strategies: $\{A_1,A_2,\dots A_N\}$

Preferences: $\{a_1,a_2,\dots a_n\},a_1\in A_1,a_2\in A_2...$