American Institute of Mathematical Sciences

Advanced
August  2004, 4(3): 575-587. doi: 10.3934/dcdsb.2004.4.575

The dynamics of public goods

Christoph Hauert 1, , Nina Haiden 2, and  Karl Sigmund 2,

1. 

Departments of Zoology and Mathematics, University of British Columbia, Vancouver, Canada V6T 1Z4, Canada
2. 

Department of Mathematics, University of Vienna, Strudlhofgasse 4, A-1090 Vienna, Austria, Austria

Received  December 2002 Revised  October 2003 Published  May 2004

We analyze the replicator equation for two games closely related with the social dilemma occurring in public goods situations. In one case, players can punish defectors in their group. In the other case, they can choose not to take part in the game. In both cases, interactions are not pairwise and payoffs non-linear. Nevertheless, the qualitative dynamics can be fully analyzed. The games offer potential solutions for the problem of the emergence of cooperation in sizeable groups of non-related individuals -- a basic question in evolutionary biology and economics.
Keywords: replicator dynamics., public goods games, Evolutionary game theory.
Mathematics Subject Classification: 91A06, 91A10, 91A22, 92D2.
Citation: Christoph Hauert, Nina Haiden, Karl Sigmund. The dynamics of public goods. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 575-587. doi: 10.3934/dcdsb.2004.4.575
[1]

Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic & Related Models, 2021, 14 (1) : 115-148. doi: 10.3934/krm.2020051
[2]

Eric Foxall. Boundary dynamics of the replicator equations for neutral models of cyclic dominance. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1061-1082. doi: 10.3934/dcdsb.2020153
[3]

Ebraheem O. Alzahrani, Muhammad Altaf Khan. Androgen driven evolutionary population dynamics in prostate cancer growth. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020426
[4]

Wenrui Hao, King-Yeung Lam, Yuan Lou. Ecological and evolutionary dynamics in advective environments: Critical domain size and boundary conditions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 367-400. doi: 10.3934/dcdsb.2020283
[5]

Laura Aquilanti, Simone Cacace, Fabio Camilli, Raul De Maio. A Mean Field Games model for finite mixtures of Bernoulli and categorical distributions. Journal of Dynamics & Games, 2020  doi: 10.3934/jdg.2020033
[6]

Shipra Singh, Aviv Gibali, Xiaolong Qin. Cooperation in traffic network problems via evolutionary split variational inequalities. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020170
[7]

Martin Kalousek, Joshua Kortum, Anja Schlömerkemper. Mathematical analysis of weak and strong solutions to an evolutionary model for magnetoviscoelasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 17-39. doi: 10.3934/dcdss.2020331
[8]

Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020451
[9]

Kung-Ching Chang, Xuefeng Wang, Xie Wu. On the spectral theory of positive operators and PDE applications. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3171-3200. doi: 10.3934/dcds.2020054
[10]

Yueyang Zheng, Jingtao Shi. A stackelberg game of backward stochastic differential equations with partial information. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020047
[11]

David W. K. Yeung, Yingxuan Zhang, Hongtao Bai, Sardar M. N. Islam. Collaborative environmental management for transboundary air pollution problems: A differential levies game. Journal of Industrial & Management Optimization, 2021, 17 (2) : 517-531. doi: 10.3934/jimo.2019121
[12]

Pierre-Etienne Druet. A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020458
[13]

Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024
[14]

Tuoc Phan, Grozdena Todorova, Borislav Yordanov. Existence uniqueness and regularity theory for elliptic equations with complex-valued potentials. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1071-1099. doi: 10.3934/dcds.2020310
[15]

Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020347
[16]

Alain Bensoussan, Xinwei Feng, Jianhui Huang. Linear-quadratic-Gaussian mean-field-game with partial observation and common noise. Mathematical Control & Related Fields, 2021, 11 (1) : 23-46. doi: 10.3934/mcrf.2020025
[17]

Qingfeng Zhu, Yufeng Shi. Nonzero-sum differential game of backward doubly stochastic systems with delay and applications. Mathematical Control & Related Fields, 2021, 11 (1) : 73-94. doi: 10.3934/mcrf.2020028
[18]

Zhongbao Zhou, Yanfei Bai, Helu Xiao, Xu Chen. A non-zero-sum reinsurance-investment game with delay and asymmetric information. Journal of Industrial & Management Optimization, 2021, 17 (2) : 909-936. doi: 10.3934/jimo.2020004
[19]

Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, 2021, 20 (1) : 449-465. doi: 10.3934/cpaa.2020276
[20]

Jann-Long Chern, Sze-Guang Yang, Zhi-You Chen, Chih-Her Chen. On the family of non-topological solutions for the elliptic system arising from a product Abelian gauge field theory. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3291-3304. doi: 10.3934/dcds.2020127

2019 Impact Factor: 1.27

Tools

Metrics

  • PDF downloads (33)
  • HTML views (0)
  • Cited by (20)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences