Abstract
Whether or not cooperation is favored over defection in evolutionary games can be assigned by structure coefficients for any arrangement of cooperators and defectors on any network modeled as a regular graph. We study how these structure coefficients relate to a scaling of dilemma strength in social dilemma games. It is shown that some graphs permit certain arrangements of cooperators and defectors to possess particularly large structure coefficients. Moreover, these large coefficients imply particularly large sections of a bounded parameter plane spanned by a scaling of gamble–intending and risk–averting dilemma strength.
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Allen, B., Nowak, M.A.: Games on graphs. EMS Surv. Math. Sci. 1, 113–151 (2014)
Allen, B., Lippner, G., Chen, Y.T., Fotouhi, B., Momeni, N., Yau, S.T., Nowak, M.A.: Evolutionary dynamics on any population structure. Nature 544, 227–230 (2017)
Broom, M., Rychtar, J.: Game-Theoretical Models in Biology. Chapman and Hall, Boca Raton (2013)
Chen, Y.T.: Sharp benefit-to-cost rules for the evolution of cooperation on regular graphs. Ann. Appl. Probab. 3, 637–664 (2013)
Chen, Y.T., McAvoy, A., Nowak, M.A.: Fixation probabilities for any configuration of two strategies on regular graphs. Sci. Rep. 6, 39181 (2016)
Hindersin, L., Traulsen, A.: Most undirected random graphs are amplifiers of selection for birth-death dynamics, but suppressors of selection for death-birth dynamics. PLoS Comput. Biol. 11, e1004437 (2015)
Nowak, M.A.: Evolutionary Dynamics: Exploring the Equations of Life. Harvard University Press, Cambridge (2006)
Perc, M., Szolnoki, A.: Coevolutionary games - a mini review. BioSystems 99, 109–125 (2010)
Richter, H.: Analyzing coevolutionary games with dynamic fitness landscapes. In: Ong, Y.S. (ed.), Proceedings of IEEE Congress on Evolutionary Computation, IEEE CEC 2016, pp. 609–616. IEEE Press, Piscataway (2016)
Richter, H.: Dynamic landscape models of coevolutionary games. BioSystems 153–154, 26–44 (2017)
Richter, H.: Properties of network structures, structure coefficients, and benefit-to-cost ratios. BioSystems 180, 88–100 (2019)
Richter, H.: Fixation properties of multiple cooperator configurations on regular graphs. Theory Biosci. 138(2), 261–275 (2019)
Shakarian, P., Roos, P., Johnson, A.: A review of evolutionary graph theory with applications to game theory. BioSystems 107, 66–80 (2012)
Szabo, G., Fath, G.: Evolutionary games on graphs. Phys. Rep. 446, 97–216 (2007)
Tanimoto, J.: A simple scaling of the effectiveness of supporting mutual cooperation in donor-recipient games by various reciprocity mechanisms. BioSystems 96, 29–34 (2009)
Tarnita, C.E., Ohtsuki, H., Antal, T., Fu, F., Nowak, M.A.: Strategy selection in structured populations. J. Theor. Biol. 259, 570–581 (2009)
Taylor, P.D., Day, T., Wild, G.: Evolution of cooperation in a finite homogeneous graph. Nature 447, 469–472 (2007)
Wang, Z., Kokubo, S., Jusup, M., Tanimoto, J.: Universal scaling for the dilemma strength in evolutionary games. Phys. Life Rev. 14, 1–30 (2015)
Zukewich, J., Kurella, V., Doebeli, M., Hauert, C.: Consolidating birth-death and death-birth processes in structured populations. PLoS One 8, e54639 (2013)
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Richter, H. (2020). Relationships Between Dilemma Strength and Fixation Properties in Coevolutionary Games. In: Liu, Y., Wang, L., Zhao, L., Yu, Z. (eds) Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. ICNC-FSKD 2019. Advances in Intelligent Systems and Computing, vol 1074. Springer, Cham. https://doi.org/10.1007/978-3-030-32456-8_27
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DOI: https://doi.org/10.1007/978-3-030-32456-8_27
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