Game Theory

Mathematical Principles & Theorems

Analyzes mathematical models of strategic interaction. Normal-form games are represented by payoff matrices \((A, B)\). A Nash Equilibrium is a strategy profile \((s_1^*, s_2^*)\) where \(u_1(s_1^*, s_2^*) \ge u_1(s_1, s_2^*)\) and \(u_2(s_1^*, s_2^*) \ge u_2(s_1^*, s_2)\). Von Neumann's Minimax Theorem for two-player zero-sum games guarantees \(\max_x \min_y x^T A y = \min_y \max_x x^T A y = V\). Models classic dilemmas: Prisoner's Dilemma, Stag Hunt, Battle of the Sexes.

Operating Instructions

• Select a classic game archetype or enter custom payoff matrix values for Player 1 and Player 2.
• Click Solve to compute Pure Strategy Nash Equilibria and Mixed Strategy probabilistic distributions.
• Inspect dominant strategy elimination steps and security value levels.
• Review strategic best-response curves on the interactive payoff canvas.