Repeated Games Summary

Game Theory · Axiom Academy

SUMMARY Repeated Games Summary Let's review the essential concepts from Unit 4 - Repeated Games Finite Repetition: Game played for T known rounds. Backward induction applies, often leading to unraveling of cooperation Infinite Repetition: Game continues indefinitely (or with unknown endpoint). Enables sustained cooperation through credible threats Key Difference: No "last period" in infinite games means future punishment remains credible Why It Matters: Real-world relationships often have indefinite duration, making infinite models more realistic Discount Factor: Parameter δ where 0 δ < 1 captures how much players value future payoffs Patient Players: High δ (near 1) means players care about the future, making cooperation sustainable Impatient Players: Low δ (near 0) means players prioritize immediate gains, favoring defection Present Value: Future payoffs are weighted by powers of δ , creating geometric series in calculations Grim Trigger: Cooperate until opponent defects, then defect forever. Harshest punishment strategy Tit-for-Tat (TFT): Copy opponent's previous action. Simple, forgiving, and often effective in experiments Credibility: Punishment phase must be a Nash equilibrium of continuation game to be believable Comparison: Grim is unforgiving but clear; TFT allows recovery from mistakes Statement: With sufficiently patient players, any feasible payoff above minmax can be sustained as subgame perfect equilibrium

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