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The Structure of a Probabilistic 1-State Transducer Representation for Prisoner’s Dilemma

  • Jeffrey TsangEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8602)

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.

Keywords

Multidimensional Scaling Unit Cube Pairwise Distance Parameter Distance Manhattan Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of GuelphGuelphCanada

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