Problem Solving Guide

Game Theory · Axiom Academy

A comprehensive step-by-step approach to solving game theory problems. Pure Strategy: Check each cell in the payoff matrix. Mark best responses for each player. Nash equilibrium occurs where both players' best responses coincide. Mixed Strategy: Use indifference conditions. Set expected payoffs equal across strategies to find mixing probabilities. Verify: Confirm no player wants to deviate unilaterally from the proposed equilibrium. Common Mistake: Don't assume every game has a pure strategy Nash equilibrium. Some only have mixed strategy equilibria. Check Each Strategy: For each player, compare payoffs across all opponent strategies. A strategy dominates if it always yields higher payoffs. Strict vs. Weak: Strict dominance requires strictly better payoffs; weak dominance allows equal payoffs in some cases. IESDS: Iteratively eliminate strictly dominated strategies to simplify the game and potentially find equilibrium. Tip: If both players have dominant strategies, their intersection is the unique Nash equilibrium. Solving Sequential Games (Backward Induction) Draw the Game Tree: Represent the game as an extensive form with decision nodes, branches for actions, and terminal payoffs. Start at the End: Begin at the terminal nodes (final outcomes) and work backwards toward the initial node. Solve Each Subgame: At each decision node, identify the optimal action for the player making the decision by comparing payoffs.

This is the written version of the interactive lesson above. See the full Game Theory course.