Game Theory & Nash Equilibrium: Prisoner Dilemma & Strategy

Game theory models strategic interaction between rational decision-makers in economics, evolutionary biology, and geopolitics.

3. Defining Nash Equilibrium

A Nash Equilibrium occurs when no player can benefit by unilaterally changing their chosen strategy while others keep theirs constant.

4. Analyzing Payoff Matrices & Mixed Strategies

In zero-sum games where one player's gain equals the opponent's loss, minimax strategy determines the optimal probabilistic mix of choices.

5. Iterated Elimination of Strictly Dominated Strategies (IESDS)

In strategic games, a strategy is "strictly dominated" if another strategy always yields a higher payoff regardless of what opponent players choose. Rational players will never play dominated strategies.

6. Evolutionary Game Theory & Stable Strategies (ESS)

In evolutionary biology, an Evolutionary Stable Strategy (ESS) is a strategy that, if adopted by a population, cannot be invaded by any alternative mutant strategy.

7. The Stag Hunt & Coordination Games

In Jean-Jacques Rousseau's Stag Hunt, two hunters must choose between hunting a stag together (high payoff, requires mutual trust) or hunting a hare individually (low payoff, guaranteed success). This illustrates the tension between risk-dominant and payoff-dominant equilibria.

8. Game Theory in Auction Design & Spectrum Bidding

Vickrey auctions (second-price sealed-bid auctions) encourage bidders to submit their true valuation of an item because the winner pays the second-highest bid. This design eliminates speculative overbidding.

9. Zero-Sum vs. Non-Zero-Sum Games

In zero-sum games (like chess, poker, or futures trading), one player's gain is exactly equal to the opponent's loss. Total utility remains constant. In non-zero-sum games (like international trade, business partnerships, or peace negotiations), win-win outcomes are possible through mutual cooperation.

10. Subgame Perfect Nash Equilibrium & Backward Induction

In sequential games represented as decision trees, Subgame Perfect Nash Equilibrium eliminates non-credible threats by analyzing the game backwards from the final decision nodes (backward induction).

11. Real-World Applications in Business Strategy & Auctions

• Price Wars (Bertrand Duopoly): Competing firms undercut prices down to marginal cost.
• Ad Spend Competition (Prisoner's Dilemma): Rival brands spend millions on advertising simply to maintain market share.
• Spectrum Frequency Auctions: Governments design multi-round combinatorial auctions to maximize taxpayer revenue while preventing collusion.