11: Game Theory
In this chapter, you will learn to:
- Solve strictly determined games.
- Solve games involving mixed strategies.
Game theory is one of the newest branches of mathematics. It first came to light when a brilliant mathematician named Dr. John von Neumann co-authored with Dr. Morgenstern a book titled Theory of Games and Economic Behavior . Since then it has played an important role in decision making in business, economics, social sciences and other fields.
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- 11.1: Strictly Determined Games
- In this chapter, we will study games that involve only two players. In these games, since a win for one person is a loss for the other, we refer to them as two-person zero-sum games. Although the games we will study here are fairly simple, they will provide us with an understanding of how games work and how they are applied in practical situations.
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- 11.2: Non-Strictly Determined Games
- In this section, we study games that have no saddle points. This means that these games do not possess a pure strategy. We call these games non-strictly determined games. If the game is played only once, it will make no difference what move is made. However, if the game is played repeatedly, a mixed strategy consisting of alternating random moves can be worked out.
Thumbnail: From an evolutionary game theory the four alternative social forms of strategic interaction. (Public Domain; Pearson Scott Foresman via Wikipedia)