Game theory is a branch of mathematics that studies strategic interactions between individuals or groups, where the outcome for each participant depends not only on their own decisions but also on the decisions of others. It provides a framework for analyzing situations in which players (decision-makers) must make choices that potentially affect one another.
Key Concepts in Game Theory:
Players: The decision-makers in the game.
Strategies: The choices available to each player.
Payoffs: The rewards or outcomes resulting from a combination of strategies.
- Games
Defined by rules and can be:
- Cooperative or Non-Cooperative: Players may collaborate or act independently.
- Zero-Sum or Non-Zero-Sum: In zero-sum games, one player’s gain is another’s loss. In non-zero-sum games, all players can gain or lose.
- Simultaneous or Sequential: Players act simultaneously or take turns.
Equilibrium: A stable state where no player can improve their outcome by changing their strategy unilaterally. The most famous is Nash Equilibrium.
Applications of Game Theory:
- Economics: Market competition, auctions, bargaining.
- Politics: Voting, conflict resolution, international relations.
- Biology: Evolutionary strategies and behaviors.
- Computer Science: Algorithm design, AI decision-making.
- Everyday Life: Negotiations, pricing strategies, and social interactions.
A classic example is the Prisoner’s Dilemma, where two individuals must decide whether to cooperate or betray, balancing personal benefit against mutual trust.