Note on Complete Proof of Axelrod's Theorem

Abstract

This note will give a complete proof of Axelrod's theorem that characterizes the advantage of Tit-for-Tat (TFT) strategy in the repeated prisoner's dilemma. Despite of its importance in Axelrod's study, the proof of the theorem is incomplete. First, the fault of the proof is depicted and two approaches for complementation are shown. Then, we provide the complete proof using these two approaches.