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Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics
1. | Center for Dynamics & Institute for Analysis, Dept. of Mathematics, Technische Universitat Dresden, 01062, Dresden, Germany, Germany |
2. | Dept. of Mathematics and NTIS, Faculty of Applied Sciences, University of West Bohemia, Univerzitni 8, 30614 Pilsen, Pilsen, Czech Republic, Czech Republic |
References:
[1] |
R. Albert and A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 74 (2002), 47-97.
doi: 10.1103/RevModPhys.74.47. |
[2] |
M. Broom and J. Rychtář, An analysis of the fixation probability of a mutant on special classes of non-directed graphs, Proc. Royal. Soc., Ser. A, 464 (2008), 2609-2627.
doi: 10.1098/rspa.2008.0058. |
[3] |
M. Broom, C. Hadjichrysanthou, J. Rychtář and B. T. Stadler, Two results on evolutionary processes on general non-directed graphs, Proc. Royal. Soc., Ser. A, 466 (2010), 2795-2798.
doi: 10.1098/rspa.2010.0067. |
[4] |
T. Clutton-Brock, Cooperation between non-kin in animal societies, Nature, 462 (2009), 51-57.
doi: 10.1038/nature08366. |
[5] |
J. Epperlein, S. Siegmund and P. Stehlík, Evolutionary games on graphs and discrete dynamical systems, J. Difference Eq. Appl., 21 (2015), 72-95.
doi: 10.1080/10236198.2014.988618. |
[6] |
W. D. Hamilton, The genetical evolution of social behaviour, J. Theor. Biol., 7 (1964), 1-16.
doi: 10.1016/0022-5193(64)90038-4. |
[7] |
C. Hauert and M. Doebeli, Spatial structure often inhibits the evolution of cooperation in the snowdrift game, Nature, 428 (2004), 643-646.
doi: 10.1038/nature02360. |
[8] |
J. Hofbauer and K. Sigmund, Evolutionary game dynamics, Bull. Amer. Math. Soc., 40 (2003), 479-519.
doi: 10.1090/S0273-0979-03-00988-1. |
[9] |
J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems, Cambridge University Press, 1988. |
[10] |
J. Libich and P. Stehlík, Monetary policy facing fiscal indiscipline under generalized timing of actions, Journal of Institutional and Theoretical Economics, 168 (2012), 393-431.
doi: 10.1628/093245612802920962. |
[11] |
J. Maynard Smith, The theory of games and the evolution of animal conflicts, Journal of Theoretical Biology, 47 (1974), 209-221.
doi: 10.1016/0022-5193(74)90110-6. |
[12] |
M. A. Nowak, Five rules for the evolution of cooperation, Science, 314 (2006), 1560-1563.
doi: 10.1126/science.1133755. |
[13] |
M. A. Nowak and R. M. May, Evolutionary games and spatial chaos, Nature, 359 (1992), 826-829.
doi: 10.1038/359826a0. |
[14] |
H. Ohtsuki and M. A. Nowak, Evolutionary games on cycles, Proc. R. Soc. B, 273 (2006), 2249-2256.
doi: 10.1098/rspb.2006.3576. |
[15] |
H. Ohtsuki and M. A. Nowak, Evolutionary stability on graphs, Journal of Theoretical Biology, 251 (2008), 698-707.
doi: 10.1016/j.jtbi.2008.01.005. |
[16] |
G. Szabó and G. Fáth, Evolutionary games on graphs, Phys. Rep., 446 (2007), 97-216.
doi: 10.1016/j.physrep.2007.04.004. |
show all references
References:
[1] |
R. Albert and A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 74 (2002), 47-97.
doi: 10.1103/RevModPhys.74.47. |
[2] |
M. Broom and J. Rychtář, An analysis of the fixation probability of a mutant on special classes of non-directed graphs, Proc. Royal. Soc., Ser. A, 464 (2008), 2609-2627.
doi: 10.1098/rspa.2008.0058. |
[3] |
M. Broom, C. Hadjichrysanthou, J. Rychtář and B. T. Stadler, Two results on evolutionary processes on general non-directed graphs, Proc. Royal. Soc., Ser. A, 466 (2010), 2795-2798.
doi: 10.1098/rspa.2010.0067. |
[4] |
T. Clutton-Brock, Cooperation between non-kin in animal societies, Nature, 462 (2009), 51-57.
doi: 10.1038/nature08366. |
[5] |
J. Epperlein, S. Siegmund and P. Stehlík, Evolutionary games on graphs and discrete dynamical systems, J. Difference Eq. Appl., 21 (2015), 72-95.
doi: 10.1080/10236198.2014.988618. |
[6] |
W. D. Hamilton, The genetical evolution of social behaviour, J. Theor. Biol., 7 (1964), 1-16.
doi: 10.1016/0022-5193(64)90038-4. |
[7] |
C. Hauert and M. Doebeli, Spatial structure often inhibits the evolution of cooperation in the snowdrift game, Nature, 428 (2004), 643-646.
doi: 10.1038/nature02360. |
[8] |
J. Hofbauer and K. Sigmund, Evolutionary game dynamics, Bull. Amer. Math. Soc., 40 (2003), 479-519.
doi: 10.1090/S0273-0979-03-00988-1. |
[9] |
J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems, Cambridge University Press, 1988. |
[10] |
J. Libich and P. Stehlík, Monetary policy facing fiscal indiscipline under generalized timing of actions, Journal of Institutional and Theoretical Economics, 168 (2012), 393-431.
doi: 10.1628/093245612802920962. |
[11] |
J. Maynard Smith, The theory of games and the evolution of animal conflicts, Journal of Theoretical Biology, 47 (1974), 209-221.
doi: 10.1016/0022-5193(74)90110-6. |
[12] |
M. A. Nowak, Five rules for the evolution of cooperation, Science, 314 (2006), 1560-1563.
doi: 10.1126/science.1133755. |
[13] |
M. A. Nowak and R. M. May, Evolutionary games and spatial chaos, Nature, 359 (1992), 826-829.
doi: 10.1038/359826a0. |
[14] |
H. Ohtsuki and M. A. Nowak, Evolutionary games on cycles, Proc. R. Soc. B, 273 (2006), 2249-2256.
doi: 10.1098/rspb.2006.3576. |
[15] |
H. Ohtsuki and M. A. Nowak, Evolutionary stability on graphs, Journal of Theoretical Biology, 251 (2008), 698-707.
doi: 10.1016/j.jtbi.2008.01.005. |
[16] |
G. Szabó and G. Fáth, Evolutionary games on graphs, Phys. Rep., 446 (2007), 97-216.
doi: 10.1016/j.physrep.2007.04.004. |
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