The undecidability of the spatialized prisoner's dilemma

Theory and Decision

Volumn 42, Issue 1, 1997, Pages 53-80

  Grim, Patrick ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

Cellular automata; Computability; Decision theory; Game theory; Prisoner's Dilemma; Undecidability

Indexed keywords

EID: 3042720238     PISSN: 00405833     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004959623042     Document Type: Article

References (24)

1. Axelrod, R.: 1984, The Evolution of Cooperation, Basic Books, New York.
2. Berlekamp, E., Conway, J., and Guy, R.: 1982, Winning Ways for your Mathematical Plays, Vol. II, Academic Press, London.
3. Boolos, G., and Jeffrey, R.: 1989, Computability and Logic, Third Edition, Cambridge Univ. Press, New York.
4. Demongeot, J., Golès, E., and Tchuente, M. (Eds.): 1985, Dynamical Systems and Cellular Automata, Academic Press, New York.
5. Dewdney, A.K.: 1990, 'The cellular automata programs that create wireworld, rugworld and other diversions', Computer Recreations, Scientific American 262(1), 146-149.
6. Dewdney, A.K.: 1993, The (New) Turing Omnibus, Computer Science Press, New York.
7. Grim, P.: 1994a, 'Computation and Undecidability in the Spatialized Prisoner's Dilemma,' Research Report No. 94-02, Group for Logic and Formal Semantics, Dept. of Philosophy, Suny at Stony Brook.
8. Grim, P.: 1994b 'An NP-Complete Question Regarding the Spatialized Prisoner's Dilemma,' Research Report No. 94-03, Group for Logic and Formal Semantics, Dept. of Philosophy, SUNY at Stony Brook.
9. Grim, P.: 1995, 'The Greater Generosity of the Spatialized Prisoner's Dilemma', Journal of Theoretical Biology 173, 353-359.
10. Grim, P.: 1996, 'Spatialization and greater generosity in the stochastic Prisoner's Dilemma', BioSystems 37, 3-17.
11. Gutowitz, H. (Ed.): 1990, Cellular Automata: Theory and Experiment, North-Holland, New York.
12. Mar, G., and St. Denis, P.: 1993a, 'The Evolution of Dynamical Meta-Strategies in the Prisoner's Dilemma', International Conference on Game Theory, SUNY at Stony Brook, July 1993, and research report No. 93-01, Group for Logic and Formal Semantics, Dept. of Philosophy, SUNY at Stony Brook.
13. Mar, G., and St. Denis, P.: 1993b, 'Chaos in Cooperation: Two-Dimensional Prisoner's Dilemmas in Infinite-Valued Logic,' research report No. 93-02, Group for Logic and Formal Semantics, Dept. of Philosophy, SUNY at Stony Brook, and International Journal of Bifurcation and Chaos 4 (1994), 943-958.
14. Minsky, M.: 1967, Computation: Finite and Infinite Machines, Prentice-Hall, Englewood Cliffs, N.J.
15. Nowak, M.: 1990, 'Stochastic Strategies in the Prisoner's Dilemma,' Theoretical Population Biology 38, 93-112.
16. Nowak, M., and May, R.: 1992, 'Evolutionary games and spatial chaos', Nature 359, 826-829.
17. Nowak, M., and May, R.: 1993, 'The Spatial Dimensions of Evolution', International Journal of Bifurcation and Chaos 3(1), 35-78.
18. Nowak, M., and Sigmund, K.: 1989, 'Game-Dynamical Aspects of the Prisoner's Dilemma', Applied Mathematics and Computation 30, 191-213.
19. Nowak, M., and Sigmund, K.: 1992, 'Tit for tat in heterogeneous populations', Nature 355, 250-252.
20. Nowak, M., and Sigmund, K.: 1993, 'A strategy of win-stay, lose-shift that out-performs tit-for-tat in the Prisoner's Dilemma game', Nature 364, 56-58.
21. Silverman, Brian.: 1987, The Phantom Fish Tank: An Ecology of Mind, Logo Computer Systems, Montreal.
22. Toffoli, T., and Margolus, N.: 1987, Cellular Automata Machines: A New Environment for Modelling, MIT Press, Cambridge, Mass.
23. Wolfram, S.: 1984, 'Cellular automata as models of complexity', Nature 311, 419-424.
24. Wolfram, S.: 1986, Theory and Applications of Cellular Automata, World Scientific, Philadelphia.