Stochastic Evolutionary Game Dynamics

Reviews of Nonlinear Dynamics and Complexity

Volumn 2, Issue , 2010, Pages 25-61

  Traulsen, Arne ^a   Hauert, Christoph ^b  

^a MAX PLANCK INSTITUTE FOR EVOLUTIONARY BIOLOGY   (Germany)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Applications; Evolution; Finite populations; Game theory; Infinite populations; Replicator dynamics; Stochastic evolutionary game dynamics

Indexed keywords

EID: 84884606549     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9783527628001.ch2     Document Type: Chapter

References (118)

1. Adams, D. (1979) The Hitchhiker's Guide to the Galaxy, Pan Books.
2. Altrock, P.M. and Traulsen, A. (2009) Fixation times in evolutionary games under weak selection. New J. Phys., 11, 013012.
3. Antal, T. and Scheuring, I. (2006) Fixation of strategies for an evolutionary game in finite populations. Bull. Math. Biol., 68, 1923-44.
4. Axelrod, R. and Hamilton, W.D. (1981) The evolution of cooperation. Science, 211, 1390-96.
5. Axelrod, R. (1984) The Evolution of Cooperation, Basic Books, New York.
6. Brandt, H., Hauert, C. and Sigmund, K. (2006) Punishing and abstaining for public goods. Proc. Natl. Acad. Sci. USA, 103, 495-97.
7. Challet, D., Marsili, M. and Zhang, Y.-C. (2004) Minority games: Interacting agents in financial markets, Oxford University Press, Oxford.
8. Challet, D. and Zhang, Y.-C. (1997) Emergence of cooperation and organization in an evolutionary game. Physica A, 246, 407-18.
9. Chalub, F.A.C.C. and Souza, M.O. (2006) The continuous limit of the Moran process and the diffusion of mutant genes in infinite populations. Math.AP/0602530.
10. Claussen, J.C. (2007) Drift reversal in asymmetric coevolutionary conflicts: influence of microscopic processes and population size. Eur. Phys. J. B., 60, 391-99.
11. Claussen, J.C. and Traulsen, A. (2008) Cyclic dominance and biodiversity in well-mixed populations. Phys. Rev. Lett., 100, 058104.
12. Clutton-Brock, T.H. and Parker, G.A. (1995) Punishment in animal societies. Nature, 373, 209-16.
13. Clutton-Brock, T.H., Brotherton, P.N.M., O'Riain, M.J., Gaynor, D., Kansky, R., Griffin, A.S. and Manser, M. (1999) Selfish sentinels in cooperative mammals. Science, 284, 1640-44.
14. Colman, A.M. (2006) The puzzle of cooperation. Nature, 440, 744-45.
15. Connor, R.C. (1995) Altruism among nonrelatives: alternatives to the "Prisoner's Dilemma". TREE, 10(2):84-6.
16. Coolen, A.C.C. (2005) The Mathematical Theory of Minority Games: Statistical Mechanics of Interacting Agents, Oxford University Press, Oxford.
17. Crow, J.F. and Kimura, M. (1970) An Introduction to Population Genetics Theory, Harper and Row, New York, NY.
18. Dawes, R.M. (1980) Social dilemmas. Ann. Rev. Psych., 31, 169-193.
19. Dieckmann, U. and Law, R. (1996) The dynamical theory of coevolution: a derivation from stochastic ecological processes. J. Math. Biol., 34, 579-612.
20. Dingli, D., Traulsen, A. and Pacheco, J.M. (2007) Stochastic dynamics of hematopoietic tumor stem cells. Cell Cycle, 6, e2-e6.
21. Doebeli, M. and Hauert, C. (2005) Models of cooperation based on the prisoner's dilemma and the snowdrift game. Ecology Letters, 8, 748-66.
22. Doebeli, M., Hauert, C. and Killingback, T. (2004) The evolutionary origin of cooperators and defectors. Science, 306, 859-62.
23. Dreber, A., Rand, D.G., Fudenberg, D. and Nowak, M.A. (2008) Winners don't punish. Nature, 452, 348-51.
24. Ewens, W.J. (2004) Mathematical Population Genetics, Springer, New York.
25. Fehr, E. and Gächter, S. (2002) Altruistic punishment in humans. Nature, 415, 137-40.
26. Fletcher, J.A. and Zwick, M. (2004) Strong altruismcan evolve in randomly formed groups. Jour. Theor. Biol., 228, 303-13.
27. Foster, K.R. and Ratnieks, F.L.W. (2000) Facultative worker policing in a wasp. Nature, 407, 692-93.
28. Fowler, J.H. (2005) Altruistic punishment and the origin of cooperation. Proc. Natl. Acad. Sci. USA, 102, 7047-49.
29. Fudenberg, D., Nowak, M.A., Taylor, C. and Imhof, L.A. (2006) Evolutionary game dynamics in finite populations with strong selection and weak mutation. Theor. Pop. Biol., 70, 352-63.
30. Gardiner, C.W. (1985) Handbook of Stochastic Methods, Springer, Berlin, 2nd edn.
31. Geritz, S.A.H., Kisdi, É., Meszéna, G. and Metz, J.A.J. (1998) Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol., 12, 35-57.
32. Gigerenzer, G. and Selten, R. (2002) Bounded Rationality, MIT Press, Cambridge, MA, USA.
33. Greig, D. and Travisano, M. (2004) The Prisoner's Dilemma and polymorphism in yeast SUC genes. Biol. Lett., 271, S25-S26.
34. Gürerk, Ö., Irlenbusch, B. and Rockenbach, B. (2006) The competitive advantage of sanctioning institutions. Science, 312, 108-111.
35. Hamilton, W.D. (1964) The genetical evolution of social behavior I and II. J. Theor. Biol., 7, 1-16 + 17-52.
36. Hamilton, W.D. (1971) The geometry of the selfish herd. J. Theor. Biol., 31, 295-311.
37. Hardin, G. (1968) The tragedy of the commons. Science, 162, 1243-48.
38. Hauert, C. (2008) VirtualLabs, http://www.univie.ac.at/virtuallabs/.
39. Hauert, C.,DeMonte, S.,Hofbauer, J. and Sigmund, K. (2002) Replicator dynamics for optional public good games. J. Theor. Biol., 218, 187-94.
40. Hauert, C., De Monte, S., Hofbauer, J. and Sigmund, K. (2002) Volunteering as red queen mechanism for cooperation in public goods games. Science, 296, 1129-32.
41. Hauert, C. and Doebeli, M. (2004) Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature, 428, 643-46.
42. Hauert, C., Holmes, M. and Doebeli, M. (2006) Evolutionary games and population dynamics:maintenance of cooperation in public goods games. Proc. Roy. Soc. Lond. B., 273, 2565-2570.
43. Hauert, C.,Michor, F.,Nowak,M.A. and Doebeli, M. (2006) Synergy and discounting of cooperation in social dilemmas. J. Theor. Biol., 239, 195-202.
44. Hauert, C. and G. Szabó (2003) Prisoner's dilemma and public goods games in different geometries: compulsory versus voluntary interactions. Complexity, 8, 31-38.
45. Hauert, C., Traulsen, A., Brandt, H., Nowak, M.A. and Sigmund, K. (2007) Via freedom to coercion: the emergence of costly punishment. Science, 316, 1905-07.
46. Hauert, C., Traulsen, A., Brandt, H., Nowak, M.A. and Sigmund, K. (2008) Public goods with punishment and abstaining in finite and infinite populations. Biological Theory, 3, 114.
47. Hauert, C.,Wakano, J.Y. andDoebeli,M. (2008) Ecological public goods games: cooperation and bifurcation. Theor. Pop. Biol., 73, 257-63.
48. Hector, A. and Bagchi, R. (2007) Biodiversity and ecosystem multifunctionality. Nature, 448, 188-91.
49. Hofbauer, J. (1996) Evolutionary dynamics for bimatrix games: A Hamiltonian system? J. Math. Biol., 34, 675-88.
50. Hofbauer, J. and Sigmund, K. (1998) Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge.
51. Holt, C.A. and Roth, A.E. (2004) The Nash equilibrium: A perspective. Proc. Natl. Acad. Sci. USA, 101, 3999-4002.
52. World Rock Paper Scissors Society, http://www.worldrps.com/.
53. Imhof, L.A., Fudenberg, D. and Nowak, M.A. (2005) Evolutionary cycles of cooperation and defection. Proc. Natl. Acad. Sci. USA, 102, 10797-800.
54. Imhof, L.A. and Nowak, M.A. (2006) Evolutionary game dynamics in a Wright Fisher process. J. Math. Biol., 52, 667-81.
55. Jackson, J.B.C. and Buss, L. (1975) Allelopathy and spatial competition among coral reef invertebrates. Proc. Natl. Acad. Sci. USA, 72, 5160-63.
56. Kagel, J.H. and Roth, A.E. (eds) (1997) The Handbook of Experimental Economics, Princeton University Press, Princeton, NJ, USA.
57. van Kampen, N.G. (1997) Stochastic Processes in Physics and Chemistry, Elsevier, Amsterdam, 2nd edn.
58. Kerr, B., Riley,M.A., Feldman, M.W. and Bohannan, B.J.M. (2002) Local dispersal promotes biodiversity in a real-life game of rock-paper-scissors. Nature, 418, 171-174.
59. Killingback, T., Doebeli, M. and Knowlton, N. (1999) Variable investment, the continuous prisoner's dilemma, and the origin of cooperation. Proc. R. Soc. Lond. B, 266, 1723-28.
60. Lessard, S. and Ladret, V. (2007) The probability of fixation of a single mutant in an exchangeable selection model. J. Math. Biol., 54, 721-44.
61. Maynard Smith, J. (1982) Evolution and the Theory of Games, Cambridge University Press, Cambridge.
62. Maynard Smith, J. and Price, G.R. (1973) The logic of animal conflict. Nature, 246, 15-18.
63. Maynard Smith, J. and Szathmáry, E. (1995) The Major Transitions in Evolution, W.H. Freeman, Oxford.
64. Metz, J.A.J., Geritz, S.A.H., Meszena, G., Jacobs, F.J.A. and van Heerwaarden, J.S. (1996) Adaptive dynamics: a geometrical study of the consequences of nearly faithful replication, in Stochastic and Spatial Structures of Dynamical Systems (eds van Strien, S.J. and Verduyn Lunel, S.M.), North Holland, Amsterdam, pp. 183-231.
65. Milinski, M. (1987) Tit for tat in sticklebacks and the evolution of cooperation. Nature, 325, 433-35.
66. Milinski, M., Semmann, D., Krambeck, H.-J. and Marotzke, J. (2006) Stabilizing the earth's climate is not a losing game: Supporting evidence from public goods experiments. Proc. Natl. Acad. Sci. USA, 103, 3994-98.
67. Milinski, M., Sommerfeld, R.D., Krambeck, H.-J., Reed, F.A. andMarotzke, J. (2008) The collective-risk social dilemma and the prevention of simulated dangerous climate change. Proc. Natl. Acad. Sci. USA, 105, 2291-94.
68. Moran, P.A.P. (1962) The Statistical Processes of Evolutionary Theory, Clarendon, Oxford.
69. Nash, J.F. (1950) Equilibrium points in n-person games. Proc. Natl. Acad. Sci. U.S.A., 36, 48-49.
70. Neu, H.C. (1992) The crisis in antibiotic resistance. Science, 257, 1064-73.
71. Nowak, M.A. (2006) Evolutionary Dynamics, Harvard University Press, Cambridge, MA, USA.
72. Nowak, M.A. (2006) Five rules for the evolution of cooperation. Science, 314, 1560-63.
73. Nowak, M.A. and May, R.M. (1992) Evolutionary games and spatial chaos. Nature, 359, 826-82.
74. Nowak, M.A., Sasaki, A., Taylor, C. and Fudenberg, D. (2004) Emergence of cooperation and evolutionary stability in finite populations. Nature, 428, 646-50.
75. Nowak, M.A. and Sigmund, K. (1990) The evolution of stochastic strategies in the prisoner's dilemma. Acta. Appl. Math., 20, 247-65.
76. Nowak, M.A. and Sigmund, K. (1998) Evolution of indirect reciprocity by image scoring. Nature, 393, 573-77.
77. Nowak, M.A. and Sigmund, K. (2004) Evolutionary dynamics of biological games. Science, 303, 793-99.
78. Ohta, T. (2002) Near-neutrality in evolution of genes and gene regulation. Proc. Natl. Acad. Sci. USA, 99, 16134-37.
79. Ohtsuki, H., Bordalo, P. and Nowak, M.A. (2007) The one-third law of evolutionary dynamics. Jour. Theor. Biol., 249, 289-95.
80. Ohtsuki, H., Hauert, C., Lieberman, E. and Nowak, M.A. (2006) A simple rule for the evolution of cooperation on graphs. Nature, 441, 502-05.
81. Pitcher, T. (1992) Who dares, wins - the function and evolution of predator inspection behavior in shoaling fish. Neth. J. Zool., 42, 371-91.
82. Rainey, P.B. and Rainey, K. (2003) Evolution of cooperation and conflict in experimental bacterial populations. Nature, 425, 72-74.
83. Reichenbach, T.,Mobilia, M. and Frey, E. (2007) Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature, 448, 1046-1049.
84. Reichenbach, T.,Mobilia, M. and Frey, E. (2007) Noise and correlations in a spatial population model with cyclic competition. Phys. Rev. Lett., 99, 238105.
85. Sandholm,W.H. (2007) Population Games and Evolutionary Dynamics, MIT Press, Cambridge, MA.
86. Sandholm,W.H. and Dokumaci, E. (2007) Dynamo: Phase diagrams for evolutionary dynamics. software suite. http://www.ssc.wisc.edu/whs/dynamo.
87. Sato, Y., Akiyama, E. and Farmer, J.D. (2002) Chaos in learning a simple twoperson game. Proc. Natl. Acad. Sci. USA, 99, 4748-51.
88. Sato, Y. and Crutchfield, J.P. (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys. Rev. E, 67, 015206(R).
89. Saunders, C.D. and Hausfater, G. (1988) The functional significance of baboon grooming behavior. Annals N.Y. Acad. Sci., 525(1), 430-32.
90. Schuster, H.G. (1995) Deterministic Chaos, VCH, Weinheim, 3rd edn.
91. Selten, R. (1990) Bounded rationality. Journal of Institutional and Theoretical Economics, 146, 649-58.
92. Semmann, D., Krambeck, H.J. and Milinski, M. (2003) Volunteering leads to rock-paper-scissors dynamics in a public goods game. Nature, 425(6956), 390-93.
93. Sigmund, K. (2007) Punish or perish? retaliation and collaboration among humans. Trends Ecol. Evol., 22(11), 593-600.
94. Sinervo, B., Chaine, A., Clobert, J., Calsbeek, R., Hazard, L., Lancaster, L., McAdam, A.G., Alonzo, S., Corrigan, G. and Hochberg, M.E. (2006) Selfrecognition, color signals, and cycles of greenbeard mutualism and altruism. Proc. Natl. Acad. Sci. USA, 103, 7372-77.
95. Sinervo, B. and Lively, C.M. (1996) The rock-paper-scissors game and the evolution of alternative male strategies. Nature, 380, 240-43.
96. Stammbach, E. and Kummer, H. (1982) Individual contributions to a dyadic interaction: An analysis of baboon grooming. Animal Behavior, 30, 964-71.
97. Storch, D., Marquet, P.A. and Brown, J.H. (eds) (2007) Scaling Biodiversity. Ecological Reviews. Cambridge University Press, Cambridge.
98. Szabó, G. and Fáth, G. (2007) Evolutionary games on graphs. Physics Reports, 446, 97-216.
99. Szabó, P., Czárán, T. and Szabó, G. (2007) Competing associations in bacterial warfare with two toxins. J. Theor. Biol., 248, 736-744.
100. Szolnoki, A. and Szabó, G. (2004) Phase transitions for rock-scissors-paper game on different networks. Phys. Rev. E, 70, 037102.
101. Taylor, C., Fudenberg, D., Sasaki, A. and Nowak, M.A. (2004) Evolutionary game dynamics in finite populations. Bull. Math. Biol., 66, 1621-44.
102. Taylor, P.D. and Jonker, L. (1978) Evolutionary stable strategies and game dynamics. Math. Biosci., 40, 145-56.
103. Tilman, D., Reich, P.B. and Knops, J.M.H. (2006) Biodiversity and ecosystem stability in a decade-long grassland experiment. Nature, 441, 629-632.
104. Traulsen, A., Claussen, J.C. and Hauert, C. (2005) Coevolutionary dynamics: From finite to infinite populations. Phys. Rev. Lett., 95, 238701.
105. Traulsen, A., Claussen, J.C. and Hauert, C. (2006) Coevolutionary dynamics in large, but finite populations. Phys. Rev. E, 74, 11901.
106. Traulsen, A. and Nowak, M.A. (2006) Evolution of cooperation by multi-level selection. Proc. Natl. Acad. Sci. USA, 103, 10952-955.
107. Traulsen, A., Nowak, M.A. and Pacheco, J.M. (2006) Stochastic dynamics of invasion and fixation. Phys. Rev. E, 74, 11909.
108. Traulsen, A., Pacheco, J.M. and Imhof, L.A. (2006) Stochasticity and evolutionary stability. Phys. Rev. E, 74, 021905.
109. Traulsen, A., Pacheco, J.M. and Nowak, M.A. (2007) Pairwise comparison and selection temperature in evolutionary game dynamics. J. Theor. Biol., 246, 522-29.
110. Traulsen, A., Röhl, T. and Schuster, H.G. (2004) Stochastic gain in population dynamics. Phys. Rev. Lett., 93, 028701.
111. Traulsen, A., Shoresh, N. and Nowak, M.A. (2008) Analytical results for individual and group selection of any intensity. Bull. Math. Biol., 70, 1410-24.
112. Trivers, R.L. (1971) The evolution of reciprocal altruism. The Quarterly Review of Biology, 46, 35-57.
113. Turner, P.E. and Chao, L. (1999) Prisoner's Dilemma in an RNA virus. Nature, 398, 441-43.
114. Turner, P.E. and Chao, L. (2003) Escape from prisoner's dilemma in RNA phage φ6. Am. Nat., 161, 497-505.
115. von Neumann, J. and Morgenstern, O. (1944) Theory of Games and Economic Behavior, Princeton University Press, Princeton, NJ, USA.
116. Wilson, D.S. (1975) A theory of group selection. Proc. Natl. Acad. Sci. USA, 72, 143-46.
117. Wilson, D.S. and Sober, E. (1994) Reintroducing group selection to the human behavioral sciences. Behavioral and Brain Sciences, 17, 585-654.
118. Zeeman, E.C. (1980) Population dynamics from game theory. Lecture Notes in Mathematics, Vol. 819, pp. 471-97.