The structure of a 3-state finite transducer representation for Prisoner's Dilemma

Abstract

To facilitate systematic and automated analysis of game playing strategies, the fingerprint, a mathematical technique that generates a functional summary independent of representation, was developed. This study attempts to push the boundaries of full state space investigation, looking at 3-state finite transducers as a representation for playing Prisoner's Dilemma. There are a staggering 23,000 unique strategies in this space, which severely limits the choice of analysis methods. These strategies are fingerprinted and pairwise distances computed, then hierarchical clustering reduces them to a manageable size for further experiments with multidimensional scaling and the mutational connectivity network. Results indicate there are no obvious cutoff scales of structure; mutational distance is not correlated with fingerprint distance; and a level of similarity with past results on smaller state spaces.