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

TL;DR

This paper presents an efficient algorithm to determine the memory depth of finite state machine strategies in the iterated prisoner's dilemma, enabling comparison with other strategy representations.

Contribution

The authors introduce a novel algorithm that accurately measures the memory depth of FSM strategies, aligning their complexity assessment with memory-n strategies.

Findings

Algorithm accurately determines FSM memory depth

Results agree with traditional strategy representations

Enables complexity comparison across different strategy forms

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.