6.7 Game Theory

The toolkit: a game = players, strategies, and payoffs (the outcome matrix); the analysis of interdependent decisions — my best move depends on yours: the mathematics of strategy (Von Neumann-Morgenstern's foundation; John Nash's equilibrium concept — the Nobel name to know).1. Dominant strategy — the best move regardless of the other's choice: if you have one, play it (the rare luxury).2. Nash equilibrium — a pair of strategies where each is the best response to the other: no player gains by unilaterally deviating — the resting point of the game (there may be several; none may be good — the crucial insight: individually rational choices can settle at collectively poor outcomes).3. The Prisoner's Dilemma (the canonical 2×2 — learn the matrix):B stays silentB confessesA silent1,1 (both light)3,0 (A heavy, B walks)A confesses0,3 (A walks, B heavy)2,2 (both medium)Whatever the other does, confessing is better (dominant for both) → the equilibrium is confess/confess (2,2) — both worse than the mutual-silence (1,1) they could have kept: individuallyrational, collectively stupid — the theorem of social life.1. The legal applications (the point of it all):cartels (each member's profitable cheat → the cartel's instability — why collusion needs enforcement, criminal or reputational: the Competition Act's economic rationale); plea bargaining (the prosecutor's game-theoretic machine — confession discounts as dominant-strategy engineering); arms races andenvironmental agreements (the treaty…