TOC
1. Introduction
Game theory is the study of mathmatical models of strategic interaction among rational decision-makers. It provides a mathematical tool for multi-person decision making.
Applications of game theory have arisen in many fileds, examples found inlucde: Oligopoly competition in industrial organization, Bargaining and auctions in microeconomics, Trade policies and international trade, Geopolitics and Networks.
2. Methodologies
2.1 Game theory v.s. Decision theory
Decision theory
- Decision theory studies the formal theory of decision-making of a single individual.
- Many theories in microeconomics belong to the region of decision theory (e.g. consumer theory, producer theory).
- In particular, decision theory can be viewed as the theory of games where there is only one individual.
- Decision theory cannot deal with strategic settings with many individuals.
Rationality
- In economics, the standard form of rationality means that a decision maker chooses an action that yields maximum (expected) utility among all possible actions, given the decision maker’s information.
- In game theory, a player is rational if the player chooses an action that maximizes his (expected) payoff, given the player’s beliefs about opponents’strategy choices.
- In this sense, game theory studies the formal theory of decision-making of rational individuals.
Philosophy
- Game theory is not descriptive but rather conditionally prescriptive. The standard game theory does not state how players do behave, but how they should behave in a certain sense.
- Most game-theoretic solution concepts tell not how people behave in practice, but how rational and intelligent agents should behave.
2.2 Non-cooperative Games
Non-cooperative game theory framework treats all players’ actions as individual actions. An individual action is determined by a player himself, independent of others in the strategic environment. The standard solution is equilibrium.
We can separate different types of non-cooperative games according to how the game is played (static v.s. dynamic) and player’s information about others (complete information v.s. incomplete information).
- Static means one-shot and simultaneous-move.
- Complete information means each player’s payoff function is common knowledge among all players.
Classification
Four types of non-cooperative games we consider:
- Static games with complete information
- Dynamic games with complete information
- Static games with incomplete information
- Dynamic games with incomplete information
And four corresponding solution concepts:
- Nash equilibrium 纳什均衡
- Subgame perfect Nash equilibrium 子博弈精炼均衡
- Bayesian Nash equibrium 贝叶斯纳什均衡
- Perfect Bayesian equilibrium 精炼贝叶斯均衡
2.3 Knowledge
Mutual knowledge (相互知识)
- An event that is known by all players.
- Mutual knowledge itelf does not imply anything about knowledge that anyone attributes to anyone else.
Common knowledge (共同知识)
- An event is said to be common knowledge among the players if all players know , all players know that they all know , all players know that they all know that they all know , and so on ad infinitum.
- An easier way to interpret this is that all players gather around a table where is displayed, so that each player can verify that the others observe and also can verify the same about everyone else.
Loading Comments...