Introduction to Game Theory/Strategic games

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Like most sciences, Game theory is an attempt to model the world in a useful and objective way. The simplest model, the strategic game, is often a suitable analog for an analysis. Strategic games have three components: a set of players, for each player a set of strategies, and a preference over which strategy to be employed for any condition. The players in the game are the same as the players in the strategic model. Each player plays the game based on the strategic preference of that particular player. 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 ...

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