The structure of a probabilistic 1-state transducer representation for prisoner’s dilemma

Abstract

In the study of evolutionary game theory, a tool called the fingerprint was developed. This mathematical technique generates a functional summary of an arbitrary game-playing strategy independent of representational details. Using this tool, this study expands the boundaries of investigating an entire small state space of strategies, to wit the probabilistic 1-state tranducers, as a representation for playing iterated Prisoner’s Dilemma. A sampled grid of 35,937 strategies out of the continuous cube was used: they are fingerprinted and pairwise distances computed. A subsampled grid of 4,913 strategies was analyzed using metric multidimensional scaling. The results show that the known 3-dimensional manifold can be embedded into around 4-5 Euclidean dimensions without self-intersection, and the curvature of the fingerprint metric with respect to standard distance is not too extreme; there is also similarity with analogous results on other state spaces.