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N-Person Game Theory: Concepts and Applications
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The Basics Of Game Theory
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Game Theory | SAGE Publications Inc
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You can view this on the NLA website. Login Register. Advanced search Search history. Browse titles authors subjects uniform titles series callnumbers dewey numbers starting from optional. See what's been added to the collection in the current 1 2 3 4 5 6 weeks months years. There is also an assumption of maximization. It is assumed that players within the game are rational and will strive to maximize their payoffs in the game.
This will exclude any "what if" questions that may arise. The number of players in a game can theoretically be infinite, but most games will be put into the context of two players. One of the simplest games is a sequential game involving two players. Below is a simple sequential game between two players. The numbers in the parentheses at the bottom of the tree are the payoffs at each respective point. The game is also sequential, so Player 1 makes the first decision left or right and Player 2 makes its decision after Player 1 up or down. Backwards induction, like all game theory, uses the assumptions of rationality and maximization, meaning that Player 2 will maximize his payoff in any given situation.
At either information set we have two choices, four in all. By eliminating the choices that Player 2 will not choose, we can narrow down our tree. In this way, we will bold the lines that maximize the player's payoff at the given information set. After this reduction, Player 1 can maximize its payoffs now that Player 2's choices are made known. The result is an equilibrium found by backwards induction of Player 1 choosing "right" and Player 2 choosing "up.
For example, one could easily set up a game similar to the one above using companies as the players. This game could include product release scenarios. If Company 1 wanted to release a product, what might Company 2 do in response? Will Company 2 release a similar competing product? By forecasting sales of this new product in different scenarios, we can set up a game to predict how events might unfold.
Below is an example of how one might model such a game.