# Introduction to Game Theory

Game Theory might be better described as Strategy Theory, or Theory of Interactive Decision Making. A *strategic situation* involves two or more interacting players who make decisions while trying to anticipate the actions and reactions by others. Game theory studies the *general principles* that explain how people and organizations act in strategic situations.

Game theory studies strategy mainly through the analysis of different "games". A "game" in game theory is a fully explicit structure which characterizes each player's set of actions, payoffs and possible outcomes under given rules of playing. Given this conditions, rational players act in such a way, that they maximize the expected value of their *von Neumann-Morgenstern Utility.* Games provide a simplified world within which to study strategy (as opposed to the real world where complexities get in the way of developing general principles).

## Table of Contents

**1** Introduction to Game Theory

### Part I - Games with Perfect Information

**2** Nash Equilibrium

- Strategic games
- Example:
*Prisoner's Dilemma* - Matrix Notation In Game Theory - How To Set Out A Game
- Example:
*Battle of the sexes*(a.k.a.*Bach or Stravinsky?*) - Example:
*Matching Pennies* - Nash equilibrium
- Best response functions
- Cournot's model of oligopoly
- Bertrand's model of oligopoly
- Auctions
- Questions
- Sources

**3** Mixed Strategy Equilibrium

- Randomization
- Mixed strategy Nash equilibrium
- Dominated actions
- Dominant Strategies
- Example: expert diagnosis
- Formation of beliefs

**4** Extensive Games with Perfect Equilibrium

- Introduction to Extensive games
- Strategies and outcomes
- Nash equilibrium
- Subgame perfect equilibrium
- Stackelberg's model of duopoly
- Adding simultaneous moves
- Adding uncertainty

**5** Coalitional Games

### Part II - Games with Imperfect Information

**6** Bayesian Games

- Motivational Examples
- Cournot's duopoly with imperfect information

**7** Extensive Games with Imperfect Information

- Strategies
- Nash equilibrium
- Beliefs
- Signaling games

### Part III - Real World Examples

**8** TV Game Shows

**9** Politics

## See Also

**Wikipedia Articles on Game Theory Related Topics**

- Game Theory article on Wikipedia
- Prisoner's Dilemma.
- John von Neumann and John Forbes Nash.
- Game semantics, an approach to establish the notion of truth in mathematical logic, in another way than Tarski did, using game theoretical concepts