Game Theory

Studies decision making between agents (players) whose outcomes depend on each other’s choices, not just their own.

Two-Person Zero-Sum Game

A game with exactly 2 players where one player’s gain equals the other’s loss; the payoffs always sum to 0.

• Payoff matrix
  Rows are one player’s strategies, columns the other’s. Entry $a_{ij}$ is the row player’s gain (equivalently, the column player’s loss) when the row player picks strategy $i$ and the column player picks strategy $j$.
• Pure strategy
  A player always picks the same single strategy.

Prisoner’s Dilemma

A 2-player, non-zero-sum game illustrating that individually rational choices can produce a jointly worse outcome than cooperation would.