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We develop an efficient algorithm to determine the memory-depth of finitestate machines and apply the algorithm to a collection of iterated prisoner'sdilemma strategies. The calculation agrees with the memory-depth of otherrepresentations of common strategies such as Tit-For-Tat, Tit-For-2-Tats, etc.which are typically represented by lookup tables. Our algorithm allows thecomplexity of finite state machine based strategies to be characterized on thesame footing as memory-n strategies.

Memory depth of finite state machine strategies for the iterated prisoner's dilemma