[Game Theory - introduction]

What is game theory

game ： Completely rational The behavior of an individual or group Direct interaction The circumstances of ;

Game theory ： Study the game , Of individuals or groups choice And this choice Result of The theory of . In short , Game theory is the theory of decision-making .

The research object of game theory ： This paper studies the decision-making when the behaviors of decision-makers interact directly and the equilibrium of this decision-making .

How to study game theory

The first assumption of game theory is that the participants are completely rational .

Completely rational ： Participants are pursuing their goals —— Utility maximization Be able to make decisions consistently , namely Participants' behaviors and goals are consistent （ Do what you want ）. Specific performance: ：

1. Participant's Preferences are consistent , And keep a clear understanding of the specific decision-making problems Stable ;
2. The decision-making problems faced by the participants have Fully understand , Even if the decision-making problem is uncertain , Participants can also describe or model this uncertainty ;
3. Participants have strong Logical reasoning ability and computing ability .

The second assumption of game theory is the structure of game problems （ Description of the game problem ） It is common knowledge to be completely rational with the participants .

The difference between common knowledge and mutual knowledge ： The former only needs everyone to know about the incident , The latter is endless mutual knowledge .

EXAMPLE：

1. Participants are rational ;
2. Every participant knows that other participants are rational ;
3. Every participant knows that every participant knows that other participants are rational .
4. …

The above expression is called rational level .

Classification of game theory

Traditionally , The game theory is divided into cooperative game and non cooperative game . The difference lies in whether the participants can reach a binding agreement in the game process .

According to the game problem itself Information structure It is divided into complete information game and incomplete information game .

The former means that all participants have a complete understanding of the information structure of the game problem , Before the game starts, all participants have no uncertainty about the game itself .

The latter means before the game begins , At least one participant is interested in one aspect of the information structure of the game problem , Not fully understood , There is prior uncertainty .

According to the participants' of the game problem itself Decision timing differences , The game can be divided into static game and dynamic game .

The former means that all participants in the game choose to act at the same time , Or although not at the same time, the latter actor does not know what action the first mover takes .

The latter refers to the sequence of the participants' actions and the participants' access to some or all of the information about the history of the game .

The solution of the game problem

The research purpose of game theory ： Find the solution of the game problem .

Definition of the solution of a game problem ： The outcome of the game predicted by all participants , That is, the consensus prediction of participants .

The nature of consistent prediction ： If all participants predict that a particular game outcome will occur , Then all participants will not use the prediction to select strategies that are inconsistent with the prediction results , namely No participant has a desire to deviate from this prediction , Therefore, this prediction result will eventually become the result of the game .