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Universal Computation in the Prisoner’s Dilemma Game

  • Conference paper
Unconventional Computation and Natural Computation (UCNC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8553))

Abstract

Previous studies of the Iterated Prisoner’s Dilemma Game (IPDG) focus on the optimal strategies for accumulating points against another player or the evolution of cooperation. Instead, this paper expands upon the possible complexity in interactions by using a Cellular Automaton (CA) model to simulate large numbers of players competing within a limited space. Unlike previous works, we introduce a method for creating a wide variety of deterministic rules by mapping each possible interaction to a binary number. We then prove the computational universality of the resulting IPDG CA. An analysis of the number of interactions leads to the discovery of interesting properties when allowing only enough iterations for a strategy to use its “transient” instructions. The implications of universal computation (UC) are also discussed.

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References

  1. Dresher, M.: Games of Strategy: Theory and Applications. Pren Hal. Appl. Math. Pren. Hal. (1961)

    Google Scholar 

  2. Axelrod, R.: The Evolution of Cooperation. Basic Books (1984)

    Google Scholar 

  3. Wolfram, S.: A New Kind of Science. Wolfram Media (2002)

    Google Scholar 

  4. Nowak, M.A., May, R.M., Sigmund, K.: The arithmetics of mutual help. Sci. Am. 272(6), 76 (1995)

    Article  Google Scholar 

  5. Nakamaru, M., Matsuda, H., Iwasa, Y.: The evolution of cooperation in a lattice-structured population. J. of Theor. Bio. 184(1), 65–81 (1997)

    Article  Google Scholar 

  6. Brauchli, K., Killingback, T., Doebeli, M.: Evolution of cooperation in spatially structured populations. J. Theor. Bio. 200(4), 405–417 (1999)

    Article  Google Scholar 

  7. Szabó, G., Antal, T., Szabó, P., Droz, M.: Spatial evolutionary prisoners dilemma game with three strategies and external constraints. Phys. Rev. E 62(1), 1095 (2000)

    Article  Google Scholar 

  8. Newth, D., Cornforth, D.: Asynchronous spatial evolutionary games. Biosystems 95(2), 120–129 (2009)

    Article  Google Scholar 

  9. Tanimoto, J., Sagara, H.: A study on emergence of alternating reciprocity in a 2 ×2 game with 2-length memory strategy. Biosystems 90(3), 728–737 (2007)

    Article  Google Scholar 

  10. Gelimson, A., Cremer, J., Frey, E.: Mobility, fitness collection, and the breakdown of cooperation. Phys. Rev. E 87(4), 042711 (2013)

    Google Scholar 

  11. Alonso-Sanz, R.: The historic prisoner’s dilemma. Int. J. Bifurcat. Chaos 9(06), 1197–1210 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. Alonso-Sanz, R.: Memory versus spatial disorder in the support of cooperation. Biosystems 97(2), 90–102 (2009)

    Article  MathSciNet  Google Scholar 

  13. Pereira, M.A., Martinez, A.S.: Pavlovian prisoner’s dilemma-analytical results, the quasi-regular phase and spatio-temporal patterns. J. Theor. Biol. 265(3), 346–358 (2010)

    Article  MathSciNet  Google Scholar 

  14. Berlekamp, E., Conway, J., Guy, R.: Winning Ways for Your Mathematical Plays, vol. 4. A.K. Peters (2004)

    Google Scholar 

  15. Nakayama, B.: Universal computation in the prisoner’s dilemma game. Undergraduate honors thesis, Regis U (2013)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Regis University, Denver, CO, 80221, USA

    Brian Nakayama

  2. Department of Physics and Computational Science, Regis University, Denver, CO, 80221, USA

    David Bahr

Authors
  1. Brian Nakayama
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  2. David Bahr
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Editor information

Editors and Affiliations

  1. Santa Barbara College of Engineering, University of California, Santa Barbara, California, USA

    Oscar H. Ibarra

  2. University of Western Ontario, London, Ontario, Canada

    Lila Kari

  3. University of Western Ontario, London, Ontario, Canada

    Steffen Kopecki

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© 2014 Springer International Publishing Switzerland

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Nakayama, B., Bahr, D. (2014). Universal Computation in the Prisoner’s Dilemma Game. In: Ibarra, O., Kari, L., Kopecki, S. (eds) Unconventional Computation and Natural Computation. UCNC 2014. Lecture Notes in Computer Science(), vol 8553. Springer, Cham. https://doi.org/10.1007/978-3-319-08123-6_24

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  • DOI: https://doi.org/10.1007/978-3-319-08123-6_24

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08122-9

  • Online ISBN: 978-3-319-08123-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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