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Published in: Dynamic Games and Applications 3/2021

17-08-2020

Structural Heterogeneity and Evolutionary Dynamics on Complex Networks

Authors: Jinhua Zhao, Xianjia Wang, Cuiling Gu, Ying Qin

Published in: Dynamic Games and Applications | Issue 3/2021

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Abstract

The study of evolutionary games on networks has revealed the impact of population structure on evolutionary dynamics. Unlike the case in well-mixed population where defection is favored by natural selection, certain types of networks have shown to favor cooperation. However, most previous research work has been focusing on frequency-based analysis, and emphasized on the update strategy adopted by each player, and thus generally considered the group of players with the same strategy as a whole. While it is powerful in deriving analytic results using this approach, the heterogeneity of players within such groups is effectively overlooked. In this paper, we attempt to emphasize more on the heterogeneity of players that comes from the network structure in evolutionary dynamics. Particularly, the prestige of a player is represented by its centrality, and it is reflected in an adapted payoff function. We provide several viable centrality measures that can be calculated using the adjacency matrix of the network. The relation between different centrality measures of the invader and the fixation of cooperation is analyzed via computational simulations. Results show that in the proposed model, compared to other three centrality measures, invaders with maximum betweenness centrality have significant advantage in terms of the fixation probability of cooperation, in both scale-free and small-world networks.

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Literature
1.
go back to reference Abramson G, Kuperman M (2001) Social games in a social network. Phys Rev E Statist Phys Plasmas Fluids Related Interdiscip Top 63(3):1–4 Abramson G, Kuperman M (2001) Social games in a social network. Phys Rev E Statist Phys Plasmas Fluids Related Interdiscip Top 63(3):1–4
2.
go back to reference Allen B, Lippner G, Chen YT, Fotouhi B, Momeni N, Yau ST, Nowak MA (2017) Evolutionary dynamics on any population structure. Nature 544(7649):227–230 CrossRef Allen B, Lippner G, Chen YT, Fotouhi B, Momeni N, Yau ST, Nowak MA (2017) Evolutionary dynamics on any population structure. Nature 544(7649):227–230 CrossRef
3.
go back to reference Amaral MA, Javarone MA (2018) Heterogeneous update mechanisms in evolutionary games: mixing innovative and imitative dynamics. Phys Rev E 97(4):16–18 CrossRef Amaral MA, Javarone MA (2018) Heterogeneous update mechanisms in evolutionary games: mixing innovative and imitative dynamics. Phys Rev E 97(4):16–18 CrossRef
4.
go back to reference Assenza S, Gómez-Gardeñes J, Latora V (2008) Enhancement of cooperation in highly clustered scale-free networks. Phys Rev E Statist Nonlinear Soft Matter Phys 78(1):1–5 CrossRef Assenza S, Gómez-Gardeñes J, Latora V (2008) Enhancement of cooperation in highly clustered scale-free networks. Phys Rev E Statist Nonlinear Soft Matter Phys 78(1):1–5 CrossRef
6.
go back to reference Bonacich P (2012) Power and centrality: a family of measures. Am J Sociol 92(5):1170–1182 CrossRef Bonacich P (2012) Power and centrality: a family of measures. Am J Sociol 92(5):1170–1182 CrossRef
8.
go back to reference Benzi M, Klymko C (2015) On the limiting behavior of parameter-dependent network centrality measures. SIAM J Matrix Anal Appl 36(2):686–706 MathSciNetMATHCrossRef Benzi M, Klymko C (2015) On the limiting behavior of parameter-dependent network centrality measures. SIAM J Matrix Anal Appl 36(2):686–706 MathSciNetMATHCrossRef
10.
go back to reference Chen YT, McAvoy A, Nowak MA (2016) Fixation Probabilities for Any Configuration of Two Strategies on Regular Graphs. Scientific Reports, 6 Chen YT, McAvoy A, Nowak MA (2016) Fixation Probabilities for Any Configuration of Two Strategies on Regular Graphs. Scientific Reports, 6
11.
12.
go back to reference Grinstead CM, Snell JL (1997) Introduction to probability. American Mathematical Society, Providence MATH Grinstead CM, Snell JL (1997) Introduction to probability. American Mathematical Society, Providence MATH
13.
go back to reference Hamilton WD (1964) The genetical evolution of social behaviour. I. J Theor Biol 7:1–16 CrossRef Hamilton WD (1964) The genetical evolution of social behaviour. I. J Theor Biol 7:1–16 CrossRef
14.
go back to reference Hauert C, Nowak MA, Lieberman E (2005) Evolutionary dynamics on graphs. Nature 433(7023):312–316 CrossRef Hauert C, Nowak MA, Lieberman E (2005) Evolutionary dynamics on graphs. Nature 433(7023):312–316 CrossRef
16.
go back to reference Li C, Zhang B, Cressman R, Tao Y (2013) Evolution of cooperation in a heterogeneous graph: fixation probabilities under weak selection. PLoS ONE 8(6):2–7 CrossRef Li C, Zhang B, Cressman R, Tao Y (2013) Evolution of cooperation in a heterogeneous graph: fixation probabilities under weak selection. PLoS ONE 8(6):2–7 CrossRef
17.
go back to reference Lien JW, Charness G, Zhang B, Li C, Yang C-L (2018) Endogenous rewards promote cooperation. Proc National Acad Sci 115(40):9968–9973 CrossRef Lien JW, Charness G, Zhang B, Li C, Yang C-L (2018) Endogenous rewards promote cooperation. Proc National Acad Sci 115(40):9968–9973 CrossRef
19.
go back to reference Negre CFA, Morzan UN, Hendrickson HP, Pal R, Lisi GP, Loria JP, Rivalta I, Ho J, Batista VS (2018) Eigenvector centrality for characterization of protein allosteric pathways. Proc National Acad Sci 115(52):E12201 LP–E12208 CrossRef Negre CFA, Morzan UN, Hendrickson HP, Pal R, Lisi GP, Loria JP, Rivalta I, Ho J, Batista VS (2018) Eigenvector centrality for characterization of protein allosteric pathways. Proc National Acad Sci 115(52):E12201 LP–E12208 CrossRef
21.
go back to reference Nowak MA (2006) Five rules for the evolution of cooperation. Science 314(5805):1560–1563 CrossRef Nowak MA (2006) Five rules for the evolution of cooperation. Science 314(5805):1560–1563 CrossRef
22.
23.
go back to reference Nowak MA, May RM (1992) Evolutionary games and spatial chaos. Nature 359(6398):826–829 CrossRef Nowak MA, May RM (1992) Evolutionary games and spatial chaos. Nature 359(6398):826–829 CrossRef
24.
go back to reference Ohtsuki H, Hauert C, Lieberman E, Nowak MA (2006) A simple rule for the evolution of cooperation on graphs and social networks. Nature 441(7092):502–505 CrossRef Ohtsuki H, Hauert C, Lieberman E, Nowak MA (2006) A simple rule for the evolution of cooperation on graphs and social networks. Nature 441(7092):502–505 CrossRef
26.
go back to reference Santos FC, Pacheco JM, Lenaerts T (2006) Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc National Acad Sci 103(9):3490–3494 CrossRef Santos FC, Pacheco JM, Lenaerts T (2006) Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc National Acad Sci 103(9):3490–3494 CrossRef
27.
go back to reference Santos FC, Rodrigues JF, Pacheco JM (2005) Epidemic spreading and cooperation dynamics on homogeneous small-world networks. Phys Rev E Statist Nonlinear Soft Matter Phys 72(5):1–5 CrossRef Santos FC, Rodrigues JF, Pacheco JM (2005) Epidemic spreading and cooperation dynamics on homogeneous small-world networks. Phys Rev E Statist Nonlinear Soft Matter Phys 72(5):1–5 CrossRef
28.
31.
go back to reference Taylor PD, Day T, Wild G (2007) Evolution of cooperation in a finite homogeneous graph. Nature 447(7143):469–472 CrossRef Taylor PD, Day T, Wild G (2007) Evolution of cooperation in a finite homogeneous graph. Nature 447(7143):469–472 CrossRef
32.
go back to reference Tomassini M, Luthi L, Giacobini M (2006) Hawks and Doves on small-world networks. Phys Rev E Statist Nonlinear Soft Matter Phys 73(1):016132 CrossRef Tomassini M, Luthi L, Giacobini M (2006) Hawks and Doves on small-world networks. Phys Rev E Statist Nonlinear Soft Matter Phys 73(1):016132 CrossRef
33.
go back to reference Trivers RLBY (1971) The evolution of reciprocal altruism. Quarterly Rev Biol 46(1):35–57 CrossRef Trivers RLBY (1971) The evolution of reciprocal altruism. Quarterly Rev Biol 46(1):35–57 CrossRef
34.
go back to reference Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(June):440–442 MATHCrossRef Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(June):440–442 MATHCrossRef
36.
go back to reference Wu J-J, Li C, Zhang B-Y, Cressman R, Tao Y (2014) The role of institutional incentives and the exemplar in promoting cooperation. Sci Rep 4:6421 CrossRef Wu J-J, Li C, Zhang B-Y, Cressman R, Tao Y (2014) The role of institutional incentives and the exemplar in promoting cooperation. Sci Rep 4:6421 CrossRef
Metadata
Title
Structural Heterogeneity and Evolutionary Dynamics on Complex Networks
Authors
Jinhua Zhao
Xianjia Wang
Cuiling Gu
Ying Qin
Publication date
17-08-2020
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 3/2021
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-020-00365-w

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