Skip to main content

Physics and Ecology of Rock-Paper-Scissors Game

Part of the Lecture Notes in Computer Science book series (LNCS,volume 2063)

Abstract

From physical and ecological aspects, we reviewan interacting particle system which follows a rule of the Rock-Paper-Scissors (RPS) game. This rule symbolically represents a food chain in ecosystems. It also represents nonequilibrium systems which have a feedback mechanism.We describe the spatial pattern dynamics in lattice RPS system: the time dependence of each species is not fully understood, especially on two-dimensional lattice. Moreover, we modify and apply RPS rule to voter and biological systems. Computer simulation for both voter model and ecosystems exhibits counter-intuitive results in phase transition. Such results can be seen in many cyclic systems, and they may be related to the unpredictability in nonequilibrium systems.

Keywords

  • Prey Density
  • Voter Model
  • Press Perturbation
  • Dimensional Lattice
  • Interact Particle System

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/3-540-45579-5_25
  • Chapter length: 12 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   99.00
Price excludes VAT (USA)
  • ISBN: 978-3-540-45579-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   129.00
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Ono, T. Igarashi, E. Ohno and M. Sasaki, Unusual thermal defence by a honeybee against mass attack by hornets. Nature, 377, 334–336 (1995).

    CrossRef  Google Scholar 

  2. B. Sinervo and C. M. Lively, The rock-paper-scissors game and the evolution of alternative male strategies. Nature, 380, 240–243 (1996).

    CrossRef  Google Scholar 

  3. R. Aelrod, The Complexity of Cooperation. (Basic Books, NewYork, 1997).

    Google Scholar 

  4. R. Aelrod and W. D. Hamilton, The evolution of cooperation. Science 211, 1390–1396 (1981).

    CrossRef  MathSciNet  Google Scholar 

  5. D. Kraines and V. Kraines, Learning to cooperate with Pavlov: an adaptive strategy for the iterated Prisoner’s Dilemma game. Theory Decision 35, 107–150 (1993).

    MATH  CrossRef  MathSciNet  Google Scholar 

  6. M. A. Nowak and K. Sigmund, A strategy of win-stay, lose-shift that outperforms tit-for tat in the Prisoner’s Dilemma game. Nature 364, 56–58 (1993).

    CrossRef  Google Scholar 

  7. K. Tainaka, Lattice model for the Lotka-Volterra system. J. Phys. Soc. Jpn. 57, 2588–2590 (1988).

    CrossRef  Google Scholar 

  8. Y. Itoh, On a ruin problem with interaction. Ann. Instit. Statst. Math. 25, 635–641 (1973).

    MATH  CrossRef  Google Scholar 

  9. Y. Itoh, Integrals of a Lotka-Volterra system of odd number of variables. Prog. Theor. Phys. 78, 507–510 (1987).

    CrossRef  Google Scholar 

  10. M. Bramson and D. Griffeath, Flux and fixation in cyclic particle systems, Ann. Probability, 17, 26–45 (1989).

    MATH  MathSciNet  CrossRef  Google Scholar 

  11. L. Frachebourg, P. L. Krapivsky and E. Ben-Naim, Segregation in a one-dimensional of interacting species. Phys. Rev. Lett. 77, 2125–2128 (1996).

    CrossRef  Google Scholar 

  12. K. Tainaka, Stationary pattern of vortices or strings in biological systems: lattice version of the Lotka-Volterra model. Phys. Rev. Lett. 63, 2688–2691 (1989).

    CrossRef  Google Scholar 

  13. K. Tainaka, Topological phase transition in biological ecosystems. Europhys. Lett. 15, 399–404 (1991).

    CrossRef  MathSciNet  Google Scholar 

  14. K. Tainaka and Y. Itoh, Apparent selforganized criticality. Phys. Lett. A 220 58–62 (1996).

    CrossRef  Google Scholar 

  15. K. Tainaka, Paradoxical effect in a 3-candidates voter model. Phys. Lett. A 176, 303–306 (1993).

    CrossRef  Google Scholar 

  16. K. Tainaka, Indirect effect in cyclic voter models. Phys. Lett. A 207 53–57 (1995).

    MATH  CrossRef  MathSciNet  Google Scholar 

  17. T. E. Harris, Contact interaction on a lattice. Ann. Prob. 2, 969–988 (1974).

    MATH  CrossRef  Google Scholar 

  18. T. M. Liggett, Interacting Particle Systems. (Springer-Verlag, NewYork, 1985).

    MATH  Google Scholar 

  19. J. Marro and R. Dickman, Nonequilibrium Phase Transition in Lattice Models (Cambridge University Press, Cambridge, 1999).

    Google Scholar 

  20. N. Nakagiri and K. Tainaka, Indirect relation between species extinction and habitat destruction. To be published in Ecol. Model.

    Google Scholar 

  21. Y. Takeuchi, Global Dynamical Properties of Lotka-Volterra System (World Scientific, Singapore, 1996).

    Google Scholar 

  22. K. Tainaka and N. Araki, Press perturbation in lattice ecosystems: parity law and optimum strategy. J. Theor. Biol. 197, 1–13. (1999).

    CrossRef  Google Scholar 

  23. J. E. Satulovsky and T. Tome, Phys. Rev. E 49, 5073 (1994).

    Google Scholar 

  24. J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems (Cambridge University Press, Cambridge, 1988).

    MATH  Google Scholar 

  25. K. Tainaka, Intrinsic uncertainty in ecological catastrophe. J. Theor. Biol. 166, 91–99 (1994).

    CrossRef  Google Scholar 

  26. D. Stauffer, Introduction to Percolation Theory (Taylor & Francis, London, 1985).

    MATH  Google Scholar 

  27. M. Sahimi, Applications of Percolation Theory (Taylor & Francis, London, 1993).

    Google Scholar 

  28. K. Kobayashi and K. Tainaka, Critical phenomena in cyclic ecosystems: parity law and selfstructuring extinction pattern. J. Phys. Soc. Jpn. 66, 38–41 (1997).

    CrossRef  Google Scholar 

  29. K. Tainaka and T. Sakata, Perturbation experiment and parity law in a cyclic ecosystem. J. Phys. Soc. Jpn. 68, 1055–1056 (1999)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tainaka, Ki. (2001). Physics and Ecology of Rock-Paper-Scissors Game. In: Marsland, T., Frank, I. (eds) Computers and Games. CG 2000. Lecture Notes in Computer Science, vol 2063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45579-5_25

Download citation

  • DOI: https://doi.org/10.1007/3-540-45579-5_25

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43080-3

  • Online ISBN: 978-3-540-45579-0

  • eBook Packages: Springer Book Archive