Abstract: We develop an efficient algorithm to determine the memory-depth of finite state machines and apply the algorithm to a collection of iterated prisoner's dilemma strategies. The calculation agrees with the memory-depth of other representations of common strategies such as Tit-For-Tat, Tit-For-2-Tats, etc. which are typically represented by lookup tables. Our algorithm allows the complexity of finite state machine based strategies to be characterized on the same footing as memory-n strategies.
@misc{gaffney2019memory,
title = {Memory depth of finite state machine strategies for the
iterated {Prisoner's Dilemma}},
author = {Gaffney, Tj and Harper, Marc and Knight, Vincent A.},
year = {2019},
eprint = {1912.04493},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/1912.04493},
}