What is Game Theory:

Game theory is a mathematical framework for analyzing strategic interactions between rational decision-makers. It studies how individuals, firms, or entities make choices in situations where the outcome depends not only on their own actions but also on the actions of others. Each participant (or "player") aims to maximize their payoff, considering the strategies of others.

Key concepts include:
- **Players**: The decision-makers (e.g., people, companies, nations).
- **Strategies**: The possible actions or plans each player can choose.
- **Payoffs**: The outcomes (rewards or costs) resulting from the combination of strategies.
- **Games**: Scenarios like cooperative (working together) or non-cooperative (competing) interactions.
- **Equilibrium**: A state where no player can improve their payoff by unilaterally changing their strategy, like the Nash Equilibrium.

For example, in the classic **Prisoner's Dilemma**, two suspects must decide whether to confess or stay silent. If both stay silent, they get light sentences (cooperation). If one confesses and the other doesn't, the confessor goes free while the other gets a harsh penalty. If both confess, both get moderate sentences. The dilemma shows how rational self-interest can lead to worse outcomes for all, as both are incentivized to confess despite mutual silence being better overall.

Game theory is used in economics, political science, biology, and more to model scenarios like pricing wars, negotiations, or evolutionary behaviors. It assumes players are rational, but real-world applications often account for imperfect information or bounded rationality.