Introduction to Game Theory: Nash Equilibrium & Prisoner's Dilemma

How mathematical modeling of strategic interaction explains economics and biology.

What is Game Theory?

The formal mathematical analysis of decision-making where the outcome for each participant depends on the choices made by all other participants.

Components of a Game: Players, Strategies, Payoffs

The Classic Prisoner's Dilemma

Two suspects are arrested. If both cooperate (stay silent), each gets 1 year. If one defects (confesses) and the other stays silent, the confessor goes free while the silent partner gets 5 years. If both defect, both get 3 years.

Strictly Dominant Strategy: Defection yields a strictly better payoff regardless of opponent choice.

Nash Equilibrium Explained

A set of strategies where no player can unilaterally improve their payoff by deviating from their chosen strategy while others keep theirs unchanged.

Equilibrium Point: (Defect, Defect) is the unique Nash Equilibrium

Real-World Applications

Telecom wireless spectrum auctions, international treaty negotiations, oligopoly pricing wars, and evolutionary biology cooperation dynamics are governed by game theory.

Zero-Sum Games: Player 1 Gain + Player 2 Loss = 0

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