What is Game theory

The Concept of Game Theory in AI

Game theory is a tool used in artificial intelligence (AI) to study the behavior of decision makers who have conflicting interests. It has its roots in economics where it was used to study the behavior of firms in oligopoly markets. However, because of its applications to decision-making problems with multiple stakeholders, it has found its way into AI and other fields.

In game theory, the decision makers are called players, and the decision they make is called a move. Games can be characterized by their rules, objectives, and actions. The rules define what actions are permissible, the objectives define what the players are trying to achieve, and the actions represent the moves available to the players.

Game theory provides a framework to understand and analyze the behavior of the players, the strategies they adopt, and the outcomes that result from these strategies.

Types of Games

There are different types of games which can be categorized based on their characteristics. Some of the common types of games include:

  • Cooperative Game: This is a game where players work together to achieve a common goal. They coordinate their strategies and the outcome is determined by how well they work together.
  • Non-Cooperative Game: In this type of game, players act independently and do not work together. Each player is trying to maximize their payoff, and the outcome is determined by their individual strategies.
  • Zero-Sum Game: This is a game where the interests of one player are directly opposed to the interest of the other player. The total payoff of the game is constant, and if one player gains, the other player loses.
  • Non-Zero Sum Game: In this type of game, there are possibilities for both players to achieve their objectives. The total payoff of the game is not constant, and both players can gain or lose.
Mechanism Design

Mechanism design is a subfield of game theory that studies how to design mechanisms (protocols) so that, when the players act according to their own interests, the outcome is socially desirable. A mechanism is a set of rules or a process used to facilitate the exchange of information, goods, or services.

The objective of mechanism design is to find a mechanism that incentivizes the players to act in a way that benefits the society as a whole. For example, in an auction, the mechanism is designed to encourage bidders to reveal their true value for the item being auctioned, so that the highest bidder wins and the seller gets the maximum value for the item. Similarly, in a voting system, the mechanism is designed to encourage voters to vote for the candidate that is the most socially desirable.

Applications of Game Theory in AI

Game theory has several applications in AI. Some of the common applications include:

  • Multi-Agent Systems: Game theory is used to study the behavior of agents in a multi-agent system. Agents are autonomous entities acting on behalf of the players in the game. Multi-agent systems are used in many intelligent systems, such as traffic management, supply chain management, and decision support systems.
  • Automated Negotiation Systems: Game theory is used to develop automated negotiation systems that can negotiate on behalf of the parties involved in the negotiation. These systems can be used in e-commerce, labor negotiations, and diplomatic negotiations.
  • Reinforcement Learning: Game theory is used to study the behavior of agents in a reinforcement learning system. Reinforcement learning is a type of machine learning where the agent learns by interacting with its environment and receiving feedback in the form of rewards or penalties.
  • Social Networks: Game theory is used to study the behavior of users in social networks. Social networks are complex systems consisting of many interacting agents, and game theory provides a framework for understanding the behavior of these agents.