The continuous Prisoner's Dilemma: I. Linear reactive strategies

Journal of Theoretical Biology

Volumn 200, Issue 3, 1999, Pages 307-321

  Wahl, Lindi M ^a   Nowak, Martin A ^a  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COOPERATIVE BEHAVIOR; EVOLUTIONARY BIOLOGY; PRISONER DILEMMA;

ARTICLE; COOPERATION; EVOLUTION; MODEL; NATURAL SELECTION; PRIORITY JOURNAL;

EID: 0033533712     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1999.0996     Document Type: Article

References (46)

1. ALEXANDER R. D. The Biology of Moral Systems. 1987;Aldine de Gruyter, New York.
2. AXELROD R. The Evolution of Cooperation. 1984;Basic Books (reprinted 1989 in Penguin, Harmondsworth), New York.
3. AXELROD R., DION D. The further evolution of cooperation. Science. 242:1988;1385-1390.
4. AXELROD R., HAMILTON W. D. The evolution of cooperation. Science. 211:1981;1390-1396.
5. BOYD R. Is the repeated Prisoner's Dilemma a good model of reciprocal altruism? Ethol. Sociobiol. 9:1988;278-305.
6. BOYD R., LORBERBAUM J. P. No pure strategy is evolutionarily stable in the repeated Prisoner's Dilemma. Nature. 327:1987;58-59.
7. BULL J. J., RICE W. R. Distinguishing mechanisms for the evolution of cooperation. J. theor. Biol. 149:1991;63-74.
8. CROWLEY P. H. Evolving cooperation: Strategies as hierarchies of rules. Biosystems. 37:1996;67-80.
9. CROWLEY P. H., PROVENCHER L., SLOANE S., DUGATKIN L. A., SPOHN B., ROGERS B. L., ALFIERI M. Evolving cooperation: the role of individual recognition. Biosystems. 37:1996;49-66.
10. DOEBELI M., KNOWLTON N. The evolution of interspecific mutualisms. Proc. Natl. Acad. Sci. U.S.A. 95:1998;8676-8680.
11. DUGATKIN L. A. Cooperation Among Animals: An Evolutionary Perspective. 1997;Oxford University Press, New York.
12. DUGATKIN L. A., MESTERTON-GIBBONS M. Cooperation among unrelated individuals: reciprocal altruism, by-product mutualism and group selection in fishes. Biosystems. 37:1996;19-30.
13. DUGATKIN L. A., MESTERTON-GIBBONS M., HOUSTON A. I. Beyond the Prisoner's Dilemma: toward models to discriminate among mechanisms of cooperation in nature. TREE. 7:1992;202-205.
14. FRANK S. A. The origin of synergistic symbiosis. J. theor. Biol. 176:1995;403-410.
15. FREAN M. The Prisoner's Dilemma without synchrony. Proc. R. Soc. Lond. B. 257:1994;75-79.
16. FREAN M. R. The evolution of degrees of cooperation. J. theor. Biol. 182:1996;549-559.
17. HAMILTON W. D. The evolution of altruistic behaviour. Am. Nat. 97:1963;354-356.
18. HAMILTON W. D. The genetical evolution of social behaviour. J. theor. Biol. 7:1964;1-16.
19. HOFBAUER J., SIGMUND K. Evolutionary Games and Population Dynamics. 1998;Cambridge University Press, Cambridge.
20. KILLINGBACK T., DOEBELI M., KNOWLTON N. Variable investment and the origin of cooperation. Proc. Natl. Acad. Sci. U.S.A. 1999.
21. KRAINES D., KRAINES V. Pavlov and the prisoner's dilemma. Theory Decision. 26:1989;47-79.
22. KREBS J. R., DAVIES N. B. Behavioural Ecology: An Evolutionary Approach. 1991;Blackwell Scientific, Oxford.
23. KÜLLING D., MILINSKI M. Size-dependent predation risk and partner quality in predator inspection of sticklebacks. Anim. Behav. 44:1992;949-955.
24. LINDGREN K. Evolutionary phenomena in simple dynamics. Langton C. G., Taylor C., Farmer J. D., Rasmussen S. Artificial Life II. X:1991;295-312 Santa Fe Institute for Studies in the Sciences of Complexity, Santa Fe.
25. MAY R. M. More evolution of cooperation. Nature. 327:1987;15-17.
26. MAYNARD SMITH J. Evolution and the Theory of Games. 1982;Cambridge University Press, Cambridge.
27. MESTERTON-GIBBONS M., DUGATKIN L. A. Cooperation among unrelated individuals: evolutionary factors. Q. Rev. Biol. 67:1992;267-281.
28. METZ J. A. J., GERITZ S. A. H., MESZENA G., JACOBS F. J. A., VAN HEERWAARDEN J. S. Adaptive dynamics: a geometrical study of the consequences of nearly faithful reproduction. Van Strien S. J., Verduyn Lunel S. M. Stochastic and Spatial Structures of Dynamical Systems. 1996;183-231 North Holland, Amsterdam.
29. MILINSKI M. Tit for tat in sticklebacks and the evolution of cooperation. Nature. 325:1987;433-435.
30. MILINSKI M., KÜLLING D., KETTLER R. Tit for tat: sticklebacks (Gasterosteus aculeatus) "trusting" a cooperating partner. Behav. Ecol. 1:1990;7-11.
31. MOLANDER P. The optimal level of generosity in a selfish, uncertain environment. J. Conflict Resolution. 29:1985;611-618.
32. NOWAK M. A., MAY R. M. Evolutionary games and spatial chaos. Nature. 359:1992;826-829.
33. NOWAK M. A., SIGMUND K. The evolution of reactive strategies in iterated games. Acta Applicandae Math. 20:1990;247-265.
34. NOWAK M. A., SIGMUND K. Tit for tat in heterogeneous populations. Nature. 355:1992;250-252.
35. NOWAK M. A., SIGMUND K. Win-stay, lose-shift outperforms tit-for-tat. Nature. 364:1993;56-58.
36. NOWAK M. A., SIGMUND K. The alternating Prisoner's Dilemma. J. theor. Biol. 168:1994;219-226.
37. NOWAK M. A., SIGMUND K. The dynamics of indirect reciprocity. J. theor. Biol. 194:1998;561-574.
38. PACKER C. Reciprocal altruism in Papio anubis. Nature. 265:1977;441-443.
39. PECK J., FELDMAN M. The evolution of helping in large, randomly mixed populations. Am. Nat. 127:1985;209-221.
40. RAPOPORT A., CHAMMAH A. M. Prisoner's Dilemma. 1965;University of Michigan Press, Ann Arbor.
41. ROBERTS G., SHERRATT T. N. Development of cooperative relationships through increasing investment. Nature. 394:1998;175-179.
42. SELTEN R., HAMMERSTEIN P. Gaps and Harley argument on evolutionary stable learning rules and in the logic of tit for tat. Th. Behav. Brain Sci. 7:1984;115-116.
43. SMALE S. The Prisoner's Dilemma and dynamical systems associated to non-cooperative games. Econometrica. 48:1980;1617-1634.
44. TRIVERS R. L. The evolution of reciprocal altruism. Q. Rev. Biol. 46:1971;35-57.
45. VERHOEFF T. A continuous version of the Prisoner's Dilemma. Computing Science Note 93/02. 1993;Eindhoven University of Technology, Eindhoven.
46. WILKINSON G. S. Reciprocal food-sharing in the vampire bat. Nature. 308:1984;181-184.