Backward Induction Examples

Game Theory · Axiom Academy

EXAMPLE Backward Induction Examples Unit 3 - Sequential Games: Mastering backward induction to find subgame perfect equilibria Excellent work! You've mastered backward induction. Here's what we learned: Backward Induction Algorithm: Start at the final decision nodes and work backward, determining optimal actions at each stage based on rational play in subsequent stages. Subgame Perfect Equilibrium (SPE): The strategy profile obtained through backward induction is always a SPE because it specifies optimal actions in every subgame, including off-equilibrium paths. Credible Threats: Only threats that are credible (i.e., part of a subgame perfect strategy) matter. Empty threats that wouldn't actually be carried out are ignored in backward induction. Market Applications: Entry-deterrence games show that incumbent firms must commit to credible responses. If fighting entry is not profitable ex-post, the threat lacks credibility. Multi-Player Extensions: Backward induction extends naturally to games with more than two players. Each player optimizes at their decision nodes given anticipated future play. Equilibrium vs. Off-Path: The SPE specifies behavior both on the equilibrium path (what actually happens) and off the equilibrium path (what would happen if someone deviated). Both are essential for credibility. This technique is fundamental for analyzing sequential games in economics, political science, and business strategy. Practice with different game trees to build intuition!

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