Table of Contents
Game Theory.
John von Neumann
Basic Elements of a Game
- Decision-maker: the person who makes the first choice.
- Opponent: the person who chooses later.
- Biological affinity for order: a tendency for organisms to actively seek and approach order.
- Players: the participants in a game.
- Strategies.
- Gains and losses: determined by a function of the combination of strategies chosen by the players—the payoff function.
- Order: when the order of decisions changes, the outcome may change even if the other elements remain the same.
Defining Game Theory
- Mathematical analysis requires a complete axiomatic system. At the end of the chain of logical reasoning, mathematical symbols must be translated back into things in the real world.
- Game outcomes and systems for attributing responsibility.
Historical Development
- The Art of War.
- Nash equilibrium: an equilibrium in a non-cooperative game; an equilibrium pair of strategies.
- The Game Theory Bible.
- Theory of Games and Economic Behavior.
Types of Games
Binding Agreements
- Cooperative games: binding agreements are possible.
- Non-cooperative games: no binding agreements; common in economics.
| Game type | Equilibrium concept |
|---|---|
| Static game with complete information | Nash equilibrium |
| Static game with incomplete information | Bayesian Nash equilibrium |
| Dynamic game with complete information | Subgame-perfect Nash equilibrium |
| Dynamic game with incomplete information | Perfect Bayesian equilibrium |
Timing of Decisions
- Static games: players who act later do not know the earlier players' choices. Example: the prisoner's dilemma.
- Dynamic games: examples include board games and card games.
Available Information
- Games with complete information.
- Games with incomplete information.
Number of Rounds and Duration
- Finite games.
- Infinite games.
Representation
- Strategic-form games.
- Extensive-form games.
Why Game Theory Matters
- Game theory in price wars.
- Game theory in pollution.
- Game theory in trade wars.
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