The structure of a depth-3 lookup table representation for Prisoner´s Dilemma

Fingerprinting is a mathematical technique that generates a representation-independent functional signature for a game-playing agent, allowing for systematic and automated analysis of strategies. In this study, the global structure and mutational connectivity network for a depth-3 lookup table with prior move history playing Prisoner´s Dilemma is investigated at different choices of the time-scale parameter in the fingerprinting operator. All 2048 strategies are fingerprinted and pairwise distances computed, then principal components analysis and hierarchical clustering used to explore the time-scale-dependent structure; Hamming versus fingerprint distance and cluster-based mutational probabilities for the connectivity network. Results indicate well-separated clusters at very short scales, rearranging into different separated clusters at very long scales, with many indistinct ones in between; the fingerprint distance is not correlated with mutational distance.