American Institute of Mathematical Sciences

Advanced
January  2012, 11(1): 375-386. doi: 10.3934/cpaa.2012.11.375

Spatiotemporal dynamics of cooperation and spite behavior by conformist transmission

Joe Yuichiro Wakano 1,

1. 

Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 1-1-1 Higashi Mita, Tama-ku, Kawasaki, Kanagawa 214-8571, Japan

Received  December 2009 Revised  August 2010 Published  September 2011

In this paper, we propose a model describing the dynamics of human society. Then we show that classic theorems on traveling wave solutions in a reaction diffusion equation can be readily applied and we obtain some mathematical result. Our model considers a human society where people play a two-strategy multi-player game. The key concepts are 1) payoff-dependent update rule of strategy and 2) social learning with conformism. Because of conformism, the system can be bistable and our primary concern is whether one global majority appears or not when multiple societies that initially have different local majorities are spatially connected. Applying the result of this general framework to a public goods game example, we show that cooperation is less likely maintained by conformism and that the spread of irrational spite behavior can occur.
Keywords: game theory., traveling wave solution, Reaction diffusion equation.
Mathematics Subject Classification: Primary: 35Q91, 35Q9.
Citation: Joe Yuichiro Wakano. Spatiotemporal dynamics of cooperation and spite behavior by conformist transmission. Communications on Pure & Applied Analysis, 2012, 11 (1) : 375-386. doi: 10.3934/cpaa.2012.11.375
References:
[1]

J. Y. Wakano, K. Aoki and M. W. Feldman, Evolution of social learning: a mathematical analysis,, Theoretical Population Biology, 66 (2004), 249.  doi: 10.1016/j.tpb.2004.06.005.  Google Scholar

[2]

J. Y. Wakano and K. Aoki, Do social learning and conformist bias coevolve? Henrich and Boyd revisited,, Theoretical Population Biology, 72 (2007), 504.  doi: 10.1016/j.tpb.2007.04.003.  Google Scholar

[3]

J. Y. Wakano and K. Aoki, A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment,, Theoretical Population Biology, 70 (2006), 486.  doi: 10.1016/j.tpb.2006.04.003.  Google Scholar

[4]

K. Aoki, J. Y. Wakano and M. W. Feldman, The emergence of social learning in a temporally changing environment: A theoretical model,, Current Anthropology, 46 (2005), 334.  doi: 10.1086/428791.  Google Scholar

[5]

W. Nakahashi, The evolution of conformist transmission in social learning when the environment changes periodically,, Theoretical Population Biology, 72 (2007), 52.  doi: 10.1016/j.tpb.2007.03.003.  Google Scholar

[6]

J. Y. Wakano, A mathematical analysis on public goods games in the continuous space,, Mathematical Biosciences, 201 (2006), 72.  doi: 10.1016/j.mbs.2005.12.015.  Google Scholar

[7]

J. Y. Wakano, Evolution of cooperation in spatial public goods games with common resource dynamics,, Journal of Theoretical Biology, 247 (2007), 616.  doi: 10.1016/j.jtbi.2007.04.008.  Google Scholar

[8]

Y. Iwasa, T. Uchida and H. Yokomizo, Nonlinear behavior of the socio-economic dynamics for lake eutrophication control,, Ecological Economics, 63 (2007), 219.  doi: 10.1016/j.ecolecon.2006.11.003.  Google Scholar

[9]

J. Henrich and R. Boyd, The evolution of conformist transmission and the emergence of between-group differences,, Evolution and Human Behavior, 19 (1998), 215.  doi: 10.1016/S1090-5138(98)00018-X.  Google Scholar

[10]

T. Kameda and D. Nakanishi, Cost-benefit analysis of social/cultural learning in a nonstationary uncertain environment: an evolutionary simulation and an experiment with human subjects,, Evolution and Human Behavior, 23 (2002), 373.  doi: 10.1016/S1090-5138(02)00101-0.  Google Scholar

[11]

R. McElreath, M. Lubell, P. J. Richerson, T. M. Waring, W. Baum, E. Edsten, C. Efferson and B. Paciotti, Applying evolutionary models to the laboratory study of social learning,, Evolution and Human Behavior, 26 (2005), 483.  doi: 10.1016/j.evolhumbehav.2005.04.003.  Google Scholar

[12]

J. Henrich, Cultural group selection, coevolutionary processes and large-scale cooperation,, Journal of Economic Behavior and Organization, 53 (2004), 3.  doi: 10.1016/S0167-2681(03)00094-5.  Google Scholar

[13]

Y. Iwasa, M. Nakamaru and S. A. Levin, Allelopathy of bacteria in a lattice population: Competition between colicin-sensitive and colicin-producing strains,, Evolutionary Ecology, 12 (1998), 785.  doi: 10.1023/A:1006590431483.  Google Scholar

[14]

J. Y. Wakano, M. A. Nowak and C. Hauert, Spatial dynamics of ecological public goods,, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 7910.  doi: 10.1073/pnas.0812644106.  Google Scholar

[15]

S. A. Levin, Dispersion and population interactions,, American Naturalist, 108 (1974), 207.  doi: 10.1086/282900.  Google Scholar

[16]

K. Kishimoto and H. F. Weinberger, The spatial homogeneity of stable equilibria of some reaction-diffusion system on convex domains,, Journal of Differential Equations, 58 (1985), 15.  doi: 10.1016/0022-0396(85)90020-8.  Google Scholar

[17]

R. Boyd and P. J. Richerson, "Culture and the Evolutionary Process,", University of Chicago Press, (1985).   Google Scholar

[18]

P. C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to traveling wave solutions , in, (1979), 335.   Google Scholar

show all references

References:
[1]

J. Y. Wakano, K. Aoki and M. W. Feldman, Evolution of social learning: a mathematical analysis,, Theoretical Population Biology, 66 (2004), 249.  doi: 10.1016/j.tpb.2004.06.005.  Google Scholar

[2]

J. Y. Wakano and K. Aoki, Do social learning and conformist bias coevolve? Henrich and Boyd revisited,, Theoretical Population Biology, 72 (2007), 504.  doi: 10.1016/j.tpb.2007.04.003.  Google Scholar

[3]

J. Y. Wakano and K. Aoki, A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment,, Theoretical Population Biology, 70 (2006), 486.  doi: 10.1016/j.tpb.2006.04.003.  Google Scholar

[4]

K. Aoki, J. Y. Wakano and M. W. Feldman, The emergence of social learning in a temporally changing environment: A theoretical model,, Current Anthropology, 46 (2005), 334.  doi: 10.1086/428791.  Google Scholar

[5]

W. Nakahashi, The evolution of conformist transmission in social learning when the environment changes periodically,, Theoretical Population Biology, 72 (2007), 52.  doi: 10.1016/j.tpb.2007.03.003.  Google Scholar

[6]

J. Y. Wakano, A mathematical analysis on public goods games in the continuous space,, Mathematical Biosciences, 201 (2006), 72.  doi: 10.1016/j.mbs.2005.12.015.  Google Scholar

[7]

J. Y. Wakano, Evolution of cooperation in spatial public goods games with common resource dynamics,, Journal of Theoretical Biology, 247 (2007), 616.  doi: 10.1016/j.jtbi.2007.04.008.  Google Scholar

[8]

Y. Iwasa, T. Uchida and H. Yokomizo, Nonlinear behavior of the socio-economic dynamics for lake eutrophication control,, Ecological Economics, 63 (2007), 219.  doi: 10.1016/j.ecolecon.2006.11.003.  Google Scholar

[9]

J. Henrich and R. Boyd, The evolution of conformist transmission and the emergence of between-group differences,, Evolution and Human Behavior, 19 (1998), 215.  doi: 10.1016/S1090-5138(98)00018-X.  Google Scholar

[10]

T. Kameda and D. Nakanishi, Cost-benefit analysis of social/cultural learning in a nonstationary uncertain environment: an evolutionary simulation and an experiment with human subjects,, Evolution and Human Behavior, 23 (2002), 373.  doi: 10.1016/S1090-5138(02)00101-0.  Google Scholar

[11]

R. McElreath, M. Lubell, P. J. Richerson, T. M. Waring, W. Baum, E. Edsten, C. Efferson and B. Paciotti, Applying evolutionary models to the laboratory study of social learning,, Evolution and Human Behavior, 26 (2005), 483.  doi: 10.1016/j.evolhumbehav.2005.04.003.  Google Scholar

[12]

J. Henrich, Cultural group selection, coevolutionary processes and large-scale cooperation,, Journal of Economic Behavior and Organization, 53 (2004), 3.  doi: 10.1016/S0167-2681(03)00094-5.  Google Scholar

[13]

Y. Iwasa, M. Nakamaru and S. A. Levin, Allelopathy of bacteria in a lattice population: Competition between colicin-sensitive and colicin-producing strains,, Evolutionary Ecology, 12 (1998), 785.  doi: 10.1023/A:1006590431483.  Google Scholar

[14]

J. Y. Wakano, M. A. Nowak and C. Hauert, Spatial dynamics of ecological public goods,, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 7910.  doi: 10.1073/pnas.0812644106.  Google Scholar

[15]

S. A. Levin, Dispersion and population interactions,, American Naturalist, 108 (1974), 207.  doi: 10.1086/282900.  Google Scholar

[16]

K. Kishimoto and H. F. Weinberger, The spatial homogeneity of stable equilibria of some reaction-diffusion system on convex domains,, Journal of Differential Equations, 58 (1985), 15.  doi: 10.1016/0022-0396(85)90020-8.  Google Scholar

[17]

R. Boyd and P. J. Richerson, "Culture and the Evolutionary Process,", University of Chicago Press, (1985).   Google Scholar

[18]

P. C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to traveling wave solutions , in, (1979), 335.   Google Scholar

[1]

Xiaojie Hou, Yi Li, Kenneth R. Meyer. Traveling wave solutions for a reaction diffusion equation with double degenerate nonlinearities. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 265-290. doi: 10.3934/dcds.2010.26.265
[2]

Guo Lin, Haiyan Wang. Traveling wave solutions of a reaction-diffusion equation with state-dependent delay. Communications on Pure & Applied Analysis, 2016, 15 (2) : 319-334. doi: 10.3934/cpaa.2016.15.319
[3]

Zhaosheng Feng. Traveling waves to a reaction-diffusion equation. Conference Publications, 2007, 2007 (Special) : 382-390. doi: 10.3934/proc.2007.2007.382
[4]

Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189
[5]

Jiang Liu, Xiaohui Shang, Zengji Du. Traveling wave solutions of a reaction-diffusion predator-prey model. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 1063-1078. doi: 10.3934/dcdss.2017057
[6]

Bang-Sheng Han, Zhi-Cheng Wang. Traveling wave solutions in a nonlocal reaction-diffusion population model. Communications on Pure & Applied Analysis, 2016, 15 (3) : 1057-1076. doi: 10.3934/cpaa.2016.15.1057
[7]

Cheng-Hsiung Hsu, Jian-Jhong Lin. Stability analysis of traveling wave solutions for lattice reaction-diffusion equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (5) : 1757-1774. doi: 10.3934/dcdsb.2020001
[8]

Hideo Deguchi. A reaction-diffusion system arising in game theory: existence of solutions and spatial dominance. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3891-3901. doi: 10.3934/dcdsb.2017200
[9]

Bingtuan Li, William F. Fagan, Garrett Otto, Chunwei Wang. Spreading speeds and traveling wave solutions in a competitive reaction-diffusion model for species persistence in a stream. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3267-3281. doi: 10.3934/dcdsb.2014.19.3267
[10]

Kota Ikeda, Masayasu Mimura. Traveling wave solutions of a 3-component reaction-diffusion model in smoldering combustion. Communications on Pure & Applied Analysis, 2012, 11 (1) : 275-305. doi: 10.3934/cpaa.2012.11.275
[11]

Zhi-Xian Yu, Rong Yuan. Traveling wave fronts in reaction-diffusion systems with spatio-temporal delay and applications. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 709-728. doi: 10.3934/dcdsb.2010.13.709
[12]

Lianzhang Bao, Zhengfang Zhou. Traveling wave solutions for a one dimensional model of cell-to-cell adhesion and diffusion with monostable reaction term. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 395-412. doi: 10.3934/dcdss.2017019
[13]

Xiaojie Hou, Yi Li. Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 681-701. doi: 10.3934/dcds.2006.15.681
[14]

Guo Lin, Wan-Tong Li, Mingju Ma. Traveling wave solutions in delayed reaction diffusion systems with applications to multi-species models. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 393-414. doi: 10.3934/dcdsb.2010.13.393
[15]

Joaquin Riviera, Yi Li. Existence of traveling wave solutions for a nonlocal reaction-diffusion model of influenza a drift. Discrete & Continuous Dynamical Systems - B, 2010, 13 (1) : 157-174. doi: 10.3934/dcdsb.2010.13.157
[16]

Weiguo Zhang, Yan Zhao, Xiang Li. Qualitative analysis to the traveling wave solutions of Kakutani-Kawahara equation and its approximate damped oscillatory solution. Communications on Pure & Applied Analysis, 2013, 12 (2) : 1075-1090. doi: 10.3934/cpaa.2013.12.1075
[17]

Ming Mei, Yau Shu Wong. Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation. Mathematical Biosciences & Engineering, 2009, 6 (4) : 743-752. doi: 10.3934/mbe.2009.6.743
[18]

Shangbing Ai, Wenzhang Huang, Zhi-An Wang. Reaction, diffusion and chemotaxis in wave propagation. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 1-21. doi: 10.3934/dcdsb.2015.20.1
[19]

Xiaojie Hou, Wei Feng. Traveling waves and their stability in a coupled reaction diffusion system. Communications on Pure & Applied Analysis, 2011, 10 (1) : 141-160. doi: 10.3934/cpaa.2011.10.141
[20]

Jibin Li, Yi Zhang. On the traveling wave solutions for a nonlinear diffusion-convection equation: Dynamical system approach. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1119-1138. doi: 10.3934/dcdsb.2010.14.1119

2019 Impact Factor: 1.105

Tools

Metrics

  • PDF downloads (31)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences