Game Theory

Game theory is a framework for thinking about strategic decisions - situations where your best move depends on what others do.

The basic setup: players, strategies, and payoffs. Each player picks a strategy, and the combination of everyone's choices determines the outcome for each player.

Nash equilibrium is the key concept: a state where no player can improve their outcome by changing their strategy alone. Everyone is doing the best they can given what everyone else is doing. It's not necessarily optimal for anyone - just stable.

Classic scenarios:

Prisoner's Dilemma. Two prisoners can cooperate (stay silent) or defect (rat out the other). If both cooperate, light sentences. If both defect, heavy sentences. If one defects and one cooperates, the defector goes free and the cooperator gets the worst outcome. The Nash equilibrium is both defect, even though both cooperating would be better for everyone.

Chicken. Two cars drive toward each other. Swerving is embarrassing but safe. Not swerving wins if the other guy swerves, but kills both if neither does. No pure Nash equilibrium - it's about commitment and credibility.

Coordination games. Both players want to coordinate (meet at the same place, use the same standard) but there are multiple equilibria. The question is which one everyone settles on.

Game theory shows up everywhere: pricing decisions, negotiations, protocol design, auction mechanisms, evolutionary biology. The value isn't in the math so much as the mental model - forcing you to think about what others will do, not just what you want to do.