The structure of a probabilistic 2-state finite transducer representation for Prisoner´s Dilemma

Several studies have used the fingerprint, a mathematical technique that generates a representation-independent functional signature of a game playing strategy, to conduct automated analyses of spaces of strategies. This study looks at an even larger state space, namely a grid over the probabilistic 2-state finite transducers, as a representation for playing Prisoner´s Dilemma. Even using just a three-level {0, 0.5, 1} grid amounts to 100,000 representable strategies, with an immense 40,679 unique strategies within. All strategies are fingerprinted and all pairwise distances computed, then hierarchical clustering reduces this dataset to around size 10,000 for further analysis with multidimensional scaling. Results indicate that the 20-dimensional grid has no obvious cutoff scales of structure, that we can quantify several important dimensions, and a high level of similarity with past results on smaller state spaces. We also find an interesting difference between complete playing equivalence of deterministic versus probabilistic transducers.