Game Theory
Analyzing situations where your success depends on what others do.
Zero-Sum Games
One player's gain is exactly the other player's loss. Total payoff = 0.
Saddle Point: If Maximin = Minimax, the game is stable and has a pure strategy solution.
Pure vs Mixed Strategies
- Pure Strategy: Player always chooses the same action.
- Mixed Strategy: Player randomizes their actions based on probabilities to confuse the opponent.
Nash Equilibrium
A situation where no player can improve their payoff by changing their strategy alone, assuming the other player's strategy stays the same.
Two criminals are arrested. If both stay silent, they get 1 year. If one betrays, he goes free and the other gets 10 years. If both betray, they get 5 years.
The Nash Equilibrium is for both to betray, even though staying silent is better for the group.
Test Yourself
Q1: In a zero-sum game, if Player A wins 10 points, Player B: