A brief introduction to game theory

Game theory is a discipline in mathematics and economics that studies the interaction between decision makers. It involves a multi-party decision-making process in which each participant attempts to maximize his or her own interests. Here are some basic concepts of game theory:

1. Basic elements of the game:

Players: The decision-makers involved in the game can be individuals, countries, companies, etc.
Strategies: The actions or decisions each player can make in the game.
Payoffs: The impact of the outcome of the game on each player, usually represented by payoffs. Payment can be money, utility value, etc.

2. Professional classification:

Zero-Sum Games: When one player's loss of interest is equal to the interest gain of other players, it is called a zero-sum game. The change in total benefit is zero.
Non-Zero-Sum Games: The changes in the interests of the players in the game do not necessarily add up to zero, they can be positive sum, negative sum, or zero.
Cooperative Games: Players can cooperate to achieve common goals and share the benefits of cooperation.

3. Hiroden:

Prisoner's Dilemma: Describes the choices faced by two criminal suspects and emphasizes the importance of cooperation. In the case of rational individuals, the optimal choice is to betray the other party.
Nash Equilibrium: In a game, if each player has no incentive to change his strategy independently given the strategies of other players, then this Group policy constitutes a Nash equilibrium.

4. For displaying:

Game Tree: A tree structure describing possible decision sequences in a game, used to analyze different paths of the game.
Evolutionary Game Theory: Applied to biology, it studies how the strategies of individuals in a group evolve over time.
Social networks and games: Game theory is applied to study the decision-making process in social networks, including cooperation, competition, etc.

5. Game solution concept:

Dominant Strategy: If a certain strategy of a player is always better for him than other strategies, no matter what strategies other players choose, this strategy It’s the domination strategy.
Nash Equilibrium: When all players have chosen the optimal strategy, no player will have the motivation to change his strategy alone. This state is a Nash equilibrium .
Reciprocity (Tit-for-Tat): In multiple rounds of the game, cooperation is rewarded for cooperation, and betrayal is rewarded for betrayal. This strategy has important applications in games such as the Prisoner's Dilemma.

6. Game challenges and responses:

Game incompleteness: The information in the game may be incomplete, and players may know little about other players’ strategies and payouts. This leads to information asymmetries and incentive problems.
Game Dynamics: Over time, players’ strategies and payouts may change, and the dynamics of the game need to be considered.

7. Using area:

Economics: Game theory is widely used in economics, especially in the study of market competition, auction mechanisms, etc.
Computer Science: Game theory has important applications in algorithm design, artificial intelligence, distributed systems and other fields.
Biology: Used to explain and predict the behavior of living organisms, such as cooperation and competition in animal groups.
Social Sciences: Game theory is used to study interactions in social and political decision-making.

8. Enka Exposure:

Evolutionarily Stable Strategy (ESS): In biology, ESS refers to a strategy that, when it becomes dominant in a group, other possible strategies It is difficult for strategies to replace it through natural selection.
Sexual Selection Theory: Part of game theory that explains why certain traits and behaviors are retained in groups during sexual selection.

9. Collaborative collaboration:

Cooperative game: Study how players cooperate to achieve common interests and share benefits.
Core: The core in a cooperative game refers to a set of allocation plans in which no player can make himself better by changing his strategy, and each player All have acceptable payments.

10. Applications of game theory in computer science:

Algorithm design: Game theory is used to design algorithms to solve problems involving multiple decision makers, such as auctions, resource allocation, etc.
Artificial Intelligence: In intelligent agent systems, game theory is used to develop intelligent decision-making strategies, especially in multi-agent systems.
Distributed Systems: Game theory is applied to analyze and design cooperation and competition strategies in distributed systems.

11. Future development of game theory:

Quantum Game Theory: With the development of quantum computing, researchers have begun to explore game theory in the quantum environment.
Social network game: Focusing on game scenarios in social networks, study how to better understand and optimize decision-making problems in social networks.
Combining machine learning and game theory: Combine machine learning techniques with game theory to better understand and adapt to real-world decision-making scenarios.

2. Group games and social dynamics:

Group Games: Study game situations involving multiple groups, such as interactions between different countries and companies.
Social Dynamics (Social Dynamics): Game theory has important applications in studying information dissemination, cultural inheritance, and group behavior evolution in society, prompting people to better understand social system.

13. Evolutionary game and human cooperation:

Evolutionary games on complex networks: Study the impact of network structure on the dynamics of evolutionary games, especially in large-scale social networks.
Human Cooperation and Cultural Evolution: Explore the reasons for the evolution of cooperative behavior in human society and how culture shapes and transmits cooperative behavior.

14. Takuji Hirohiro:

Multi-level game theory: The study of games that occur at multiple levels, such as between individuals and groups, to more fully understand the evolution of complex systems.

15. Game theory and sustainable development:

Resource allocation and environmental game: Study how to cooperate and compete under limited resources and environmental constraints to promote sustainable development.
Applications of Game Theory in Policy Making: Use game theory models to analyze and optimize policy decisions, especially in situations involving multiple stakeholders.

16. Ethics and fair games:

Ethical considerations in game theory: How to consider values such as ethics, fairness and justice in games to promote a more equal and inclusive society.
Ethical trade-offs between cooperation and competition: In gaming situations, how do people balance individual cooperation and competition to achieve more sustainable and just outcomes.

The future development direction of game theory covers more complex social situations and applications in new fields. Researchers work to advance the theoretical and practical applications of game theory to better understand the evolution of human behavior and social systems.

Game theory is widely used in economics, computer science, biology and other fields. It provides a framework for understanding the dynamic process of interactions between decision makers and plays an important role in practical applications.