Skip to main content
SpringerLink
Log in

Automata, repeated games and noise

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

We consider two-state automata playing repeatedly the Prisoner's Dilemma (or any other 2 × 2-game). The 16 × 16-payoff matrix is computed for the limiting case of a vanishingly small noise term affecting the interaction. Some results concerning the evolution of populations of automata under the action of selection are obtained. The special role of “win-stay, lose-shift”-strategies is examined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aumann, R. (1981) Survey of repeated games, in Essays in Game Theory and Mathematical Economy in Honor of Oskar Morgenstern, Wissenschaftsverlag, Bibliographisches Institut, Mannheim

    Google Scholar 

  • Axelrod, R. (1984) The Evolution of Cooperation, Basic Books, New York (reprinted 1989 in Penguin, Harmondsworth)

    Google Scholar 

  • Axelrod, R. (1987) The evolution of strategies in the iterated Prisoner's Dilemma, in Davis, D. (ed.) Genetic Algorithms and Simulated Annealing, Pitman, London

    Google Scholar 

  • Axelrod, R. and Hamilton, W.D. (1981) The evolution of cooperation, Science 211, 1390–6

    Google Scholar 

  • Axelrod, R. and Dion, D. (1988) The further evolution of cooperation, Science 242, 1385–90

    Google Scholar 

  • Abreu, D. and Rubinstein, A. (1988) The structure of Nash equilibria in repeated games with finite automata, Econometrica 56, 1259–82

    Google Scholar 

  • Banks, J. S. and Sundaram, R. K. (1990), Repeated games, finite automata and complexity, Games and Economic Behaviour 2, 97–117

    Google Scholar 

  • Binmore, K. G. and Samuelson, L. (1992) Evolutionary stability in repeated games played by finite automata, Journal of Economic Theory 57, 278–305

    Google Scholar 

  • Boyd, R. (1989) Mistakes allow evolutionarily stability in the repeated Prisoner's Dilemma game, J. Theor. Biol. 136, 47–59

    Google Scholar 

  • Brannath, W. (1994) Heteroclinic networks, on the tetrahedron, Nonlinearity 7, 1367–1384

    Google Scholar 

  • Esam, E. (1995) The trembling hand approach to automata, to appear

  • Guyer, M. and Perkel, B. (1972) Experimental games. A bibliography 1945–71, Communication Nr. 293, Mental Health Research Inst., Univ. of Chicago

  • Hofbauer, J. and Sigmund, K. (1988) The Theory of Evolution and Dynamical Systems, Cambridge UP

  • Kraines, D. and Kraines, V. (1988) Pavlov and the Prisoner's Dilemma, Theory and Decision 26, 47–79

    Google Scholar 

  • Lindgren, K. (1991) Evolutionary phenomena in simple dynamics, in Artificial life II (ed. C. G. Langton et al), Santa Fe Institute for Studies in the Sciences of Complexity Vol. X, 295–312

  • May, R. M. (1987), More evolution of cooperation, Nature 327, 15–17

    Google Scholar 

  • Maynard Smith, J (1982) Evolution and the theory of games, Cambridge UP

  • Miller, J. H. (1989) The evolution of automata in the Repeated Prisoner's Dilemma, working paper of the Santa Fe Institute Economics Research Program

  • Nowak, M. and Sigmund, K. (1992) Tit for tat in heterogeneous populations, Nature 355, 250–2

    Google Scholar 

  • Nowak, M. and Sigmund, K. (1993a) Chaos and the evolution of cooperation, Proc. Nat. Acad. Science USA, 90, 5091–5094

    Google Scholar 

  • Nowak, M. and Sigmund, K. (1993b) Win-stay, lose-shift outperforms tit-for-tat, Nature, 364, 56–58

    Google Scholar 

  • Nowak, M. and Sigmund, K. (1994) The alternating Prisoner's Dilemma, Journal of Theoretical Biology 168, 219–226

    Google Scholar 

  • Probst, D. A. (1993) Evolution, automata and the repeated Prisoner's Dilemma, to appear

  • Rapoport, A. and Chammah, A. (1965) The Prisoner's Dilemma, Univ. of Michigan Press, Ann Arbor

    Google Scholar 

  • Rapoport, A., Guyer, M. and Gordon, D. (1976) The 2 × 2 game, Univ. of Michigan Press, Ann Arbor

    Google Scholar 

  • Rubinstein, A. (1986) Finite automata play the repeated Prisoner's Dilemma, Journal of Economic Theory 39, 83–96

    Google Scholar 

  • Selten, R. (1975) Reexamination of the perfectness concept for equilibrium points in extensive games, Int. J. Game Theory 4, 25–55

    Google Scholar 

  • Selten, R. and Hammerstein, P. (1984), Gaps in Harley's argument on evolutionarily stable learning rules and in the logic of tit for tat, Behavioural and Brains Sciences 7, 115–116

    Google Scholar 

  • Sigmund, K. (1995) Games of Life, Penguin, Harmandsworth

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Zoology, University of Oxford, South Parks Road, OX1 3PS, Oxford, U.K.

    Martin A. Nowak

  2. Institut für Mathematik, Universität Wien Strudlhofgasse 4, A-1090, Vienna, Austria

    Karl Sigmund

  3. Department of Mathematics, Ain Shames University, Abassia, Cairo, Egypt

    Esam El-Sedy

Authors
  1. Martin A. Nowak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karl Sigmund
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Esam El-Sedy
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nowak, M.A., Sigmund, K. & El-Sedy, E. Automata, repeated games and noise. J. Math. Biol. 33, 703–722 (1995). https://doi.org/10.1007/BF00184645

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00184645

Keywords

Search

Navigation