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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ashlock, D., Kim, E.-Y.: Techniques for analysis of evolved prisoner’s dilemma strategies with fingerprints. In: Proceedings of the 2005 Congress on Evolutionary Computation, pp. 2613–2620 (2005)
Ashlock, D., Kim, E.-Y., von Roeschlaub, W.K.: Fingerprints: enabling visualization and automatic analysis of strategies for two player games. In: Proceedings of the 2004 Congress on Evolutionary Computation, pp. 381–387 (2004)
Ashlock, D., Kim, E.-Y.: Fingerprinting: visualization and automatic analysis of Prisoner’s Dilemma strategies. IEEE Transactions on Evolutionary Computation 12(5), 647–659 (2008)
Ashlock, D., Kim, E.-Y., Ashlock, W.: Fingerprint analysis of the noisy Prisoner’s Dilemma using a finite state representation. IEEE Transactions on Computational Intelligence and AI in Games 1(2), 157–167 (2009)
Ashlock, D., Kim, E.-Y.: Fingerprint analysis of the noisy Prisoner’s Dilemma. In: Proceedings of the 2007 Congress on Evolutionary Computation, pp. 4073–4080 (2007)
Ashlock, D., Kim, E.-Y., Leahy, N.: Understanding representational sensitivity in the iterated Prisoner’s Dilemma with fingerprints. IEEE Transactions on Systems, Man and Cybernetics C 36(4), 464–475 (2006)
Ashlock, D., Kim, E.-Y.: The impact of cellular representation on finite state agents for Prisoner’s Dilemma. In: Proceedings of the 2005 Genetic and Evolutionary Computing Conference, pp. 59–66 (2005)
Ashlock, W., Ashlock, D.: Changes in Prisoner’s Dilemma strategies over evolutionary time with different population sizes. In: Proceedings of the Congress on Evolutionary Computation 2006, pp. 297–304 (2006)
Gibbs, A.L., Su, F.E.: On choosing and bounding probability metrics. International statistical review 70(3), 419–435 (2002)
Ishibuchi, H., Ohyanagi, H., Nojima, Y.: Evolution of strategies with different representation schemes in a spatial iterated Prisoner’s Dilemma game. IEEE Transactions on Computational Intelligence and AI in Games 3(1), 67–82 (2011)
Kruskal, J.B.: Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29(1), 1–27 (1964)
de Leeuw, J.: Applications of convex analysis to multidimensional scaling. In: Barra, J.R., et al. (eds.) Recent Developments in Statistics. pp. 133–145. North-Holland, Amsterdam, (1977)
Sneath, P.H.A., Sokal, R.R.: Numerical Taxonomy: The Principles and Practice of Numerical Classification. Freeman, CA (1973)
Stroud, A.H.: Approximate Calculation of Multiple Integrals. Englewood Cliffs, Prentice-Hall, NJ (1971)
Tsang, J.: The parametrized probabilistic finite state transducer probe game player fingerprint model. IEEE Transactions on Computational Intelligence and AI in Games 2(3), 208–224 (2010)
Tsang, J.: The structure of a depth-3 lookup table representation for Prisoner’s Dilemma. In: Proceedings of the IEEE Conference on Computational Intelligence in Games 2010, pp. 54–61 (2010)
Tsang, J.: The structure of a 3-state finite transducer representation for Prisoner’s Dilemma. In: Proceedings of the IEEE Conference on Computational Intelligence in Games 2010, pp. 307–313 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tsang, J. (2014). The Structure of a Probabilistic 1-State Transducer Representation for Prisoner’s Dilemma. In: Esparcia-Alcázar, A., Mora, A. (eds) Applications of Evolutionary Computation. EvoApplications 2014. Lecture Notes in Computer Science(), vol 8602. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45523-4_33
Download citation
DOI: https://doi.org/10.1007/978-3-662-45523-4_33
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-45522-7
Online ISBN: 978-3-662-45523-4
eBook Packages: Computer ScienceComputer Science (R0)