Backward Induction

Game Theory · Axiom Academy

Unit 3: Sequential Games - Solving extensive-form games by reasoning backwards from the end 1. The Backward Induction Algorithm Backward induction follows a systematic procedure to solve any finite sequential game: Start at the terminal nodes - Identify all endpoints of the game tree where payoffs are defined Move to the last decision node - Find the decision node immediately before the terminal nodes Choose the highest payoff - The player at this node selects the action that maximizes their payoff Replace the subtree - Collapse this decision node into a terminal node with the resulting payoff Repeat backwards - Continue this process moving backwards through the tree until reaching the initial node The animation below demonstrates this process on a simple two-player sequential game. Let's apply backward induction to a concrete game. Consider an entry game where: Player 1 (Entrant) decides whether to Enter or Stay Out of a market Player 2 (Incumbent) responds by choosing to Fight or Accommodate if entry occurs Payoffs are given as (Player 1, Player 2) at each terminal node Watch as we solve this game by starting from Player 2's decision and working backwards to find Player 1's optimal strategy. 3. Subgame Perfect Equilibrium Backward induction doesn't just find any Nash equilibrium - it finds a subgame perfect Nash equilibrium (SPNE) . Backward induction guarantees subgame perfection because: We solve each subgame starting from the smallest (terminal) subgames

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