Stochastic stability in spatial games

Journal of Statistical Physics

Volumn 117, Issue 1-2, 2004, Pages 99-110

  Miękisz, Jacek ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

cellular automata; Evolutionary game theory; Nash equilibria; stochastic stability

Indexed keywords

EID: 5444265707     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOSS.0000044065.65866.bc     Document Type: Article

References (34)

1. W. B. Arthur, S. N. Durlauf, and D. A. Lane, eds. The Economy as an Evolving Complex System II. (Addison-Wesley, Reading, MA, 1997).
2. Econophysics bulletin on www.unifr.ch/econophysics.
3. J. Weibull, Evolutionary Game Theory (MIT Press, Cambridge, MA, 1997).
4. J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, 1998).
5. J. Hofbauer and K. Sigmund, Evolutionary Game Dynamics, Bulletin AMS 40:479 (2003).
6. L. E. Blume, The statistical mechanics of strategic interaction, Games Econ. Behav. 5:387 (1993).
7. G. Ellison, Learning, local interaction, and coordination, Econometrica 61:1047 (1993).
8. H. P. Young, Individual Strategy and Social Structure: An Evolutionary Theory of Institutions (Princeton University Press, Princeton, 1998).
9. G. Ellison, Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution, Rev. Econ. Stud. 67:17 (2000).
10. R. Axelrod, The Evolution of Cooperation (Basic Books, New York, 1984).
11. M. A. Nowak and R. M. May, The spatial dilemmas of evolution, Int. J. Bifurcation Chaos 3:35 (1993).
12. M. A. Nowak, S. Bonhoeffer, and R. M. May, More spatial games, Int. J. Bifurcation Chaos 4:33-56 (1994).
13. K. Lindgren and M. G. Nordahl M. G., Evolutionary dynamics of spatial games, Physica D 75:292 (1994).
14. K. Brauchli, T. Killingback, and M. Doebeli, Evolution of cooperation in spatially structured populations, J. Theor. Biol. 200:405 (1999).
15. G. Szabó, T. Antal, P. Szabó, and M. Droz, Spatial evolutionary prisoner's dilemma game with three strategies and external constraints, Phys. Rev. E 62:1095 (2000).
16. Ch. Hauert, Effects of space in 2 x 2 games, Int. J. Bifurcation Chaos 12:1531 (2002).
17. J. Maynard Smith, The theory of games and the evolution of animal conflicts, J. Theor. Biol. 47:209 (1974).
18. J. Maynard Smith, Evolution and the Theory of Games (Cambridge, Cambridge University Press, 1982).
19. P. D. Taylor and L. B. Jonker, Evolutionarily stable strategy and game dynamics, Math. Biosci. 40:145 (1978).
20. J. Hofbauer, P. Schuster, and K. Sigmund, A note on evolutionarily stable strategies and game dynamics, J. Theor. Biol. 81:609 (1979).
21. E. Zeeman, Dynamics of the evolution of animal conflicts, J. Theor. Biol. 89:249 (1981).
22. D. Foster and P. H. Young, Stochastic evolutionary game dynamics, Theor. Popul. Biol. 38:219 (1990).
23. Y. Kim, Equilibrium selection in n-person coordination games, Games Econ. Behav. 15:203 (1996).
24. M. Broom, C. Cannings, and G. T. Vickers, Multi-player matrix games, Bull. Math. Biol. 59:931 (1997).
25. M. Bukowski and J. Miȩkisz, Evolutionary and asymptotic stability in multi-player games. Warsaw University preprint (2002), www.mimuw.edu.pl/ ~miekisz/multi.ps.
26. J. Harsányi and R. Selten, A General Theory of Equilibrium Selection in Games (MIT Press, Cambridge MA, 1988).
27. D. Monderer and L. S. Shapley, Potential games, Games Econ. Behav. 14:124 (1996).
28. T. Maruta. On the relationship between risk-dominance and stochastic stability, Games Econ. Behav. 19:221 (1977).
29. M. Freidlin and A. Wentzell, On small random perturbations of dynamical systems, Russian Math. Surveys 25:1 (1970).
30. M. Freidlin and A. Wentzell, Random Perturbations of Dynamical Systems (Springer Verlag, New York, 1984).
31. B. Shubert, A flow-graph formula for the stationary distribution of a Markov chain, IEEE Trans. Syst. Man. Cybernet. 5:565 (1975).
32. M. Kandori, G. J. Mailath, and R. Rob, Learning, mutation, and long-run equilibria in games, Econometrica 61:29 (1993).
33. P. H. Young, The evolution of conventions, Econometrica 61:57 (1993).
34. J. Miȩkisz, Statistical mechanics of evolutionary games, Warsaw University preprint (2003), www.mimuw.edu.pl/~miekisz/statmech.ps.