What is Game Theory?

Game Theory is a branch of mathematics that studies strategic interactions between rational decision-makers. It analyzes how individuals or groups make choices when their outcomes depend on others’ actions.

Key Concepts

Core elements include players (decision-makers), strategies (available choices), and payoffs (outcomes). A game can be represented as:

Where \(N\) is the set of players, \(S\) is the set of strategies, and \(U\) is the payoff function.

Examples

Consider a simple game: Two firms decide whether to lower prices. If both do, profit is 2 each; if neither does, profit is 5 each; if one does and the other doesn’t, the lower gets 6, the higher gets 1.

Applications

Game Theory applies to economics (market competition), biology (evolution), politics (voting), and more.