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

The dynamics of public goods


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


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.
Citation: Christoph Hauert, Nina Haiden, Karl Sigmund. The dynamics of public goods. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 575-587. doi: 10.3934/dcdsb.2004.4.575

Marta Faias, Emma Moreno-García, Myrna Wooders. A strategic market game approach for the private provision of public goods. Journal of Dynamics and Games, 2014, 1 (2) : 283-298. doi: 10.3934/jdg.2014.1.283


Saul Mendoza-Palacios, Onésimo Hernández-Lerma. Stability of the replicator dynamics for games in metric spaces. Journal of Dynamics and Games, 2017, 4 (4) : 319-333. doi: 10.3934/jdg.2017017


Astridh Boccabella, Roberto Natalini, Lorenzo Pareschi. On a continuous mixed strategies model for evolutionary game theory. Kinetic and Related Models, 2011, 4 (1) : 187-213. doi: 10.3934/krm.2011.4.187


Anna Lisa Amadori, Astridh Boccabella, Roberto Natalini. A hyperbolic model of spatial evolutionary game theory. Communications on Pure and Applied Analysis, 2012, 11 (3) : 981-1002. doi: 10.3934/cpaa.2012.11.981


Eduardo Espinosa-Avila, Pablo Padilla Longoria, Francisco Hernández-Quiroz. Game theory and dynamic programming in alternate games. Journal of Dynamics and Games, 2017, 4 (3) : 205-216. doi: 10.3934/jdg.2017013


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


William H. Sandholm. Local stability of strict equilibria under evolutionary game dynamics. Journal of Dynamics and Games, 2014, 1 (3) : 485-495. doi: 10.3934/jdg.2014.1.485


Jeremias Epperlein, Stefan Siegmund, Petr Stehlík, Vladimír  Švígler. Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 803-813. doi: 10.3934/dcdsb.2016.21.803


Sylvain Sorin. Replicator dynamics: Old and new. Journal of Dynamics and Games, 2020, 7 (4) : 365-386. doi: 10.3934/jdg.2020028


King-Yeung Lam. Dirac-concentrations in an integro-pde model from evolutionary game theory. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 737-754. doi: 10.3934/dcdsb.2018205


Hassan Najafi Alishah, Pedro Duarte. Hamiltonian evolutionary games. Journal of Dynamics and Games, 2015, 2 (1) : 33-49. doi: 10.3934/jdg.2015.2.33


Lianju Sun, Ziyou Gao, Yiju Wang. A Stackelberg game management model of the urban public transport. Journal of Industrial and Management Optimization, 2012, 8 (2) : 507-520. doi: 10.3934/jimo.2012.8.507


Andrzej Swierniak, Michal Krzeslak. Application of evolutionary games to modeling carcinogenesis. Mathematical Biosciences & Engineering, 2013, 10 (3) : 873-911. doi: 10.3934/mbe.2013.10.873


Ross Cressman, Vlastimil Křivan. Using chemical reaction network theory to show stability of distributional dynamics in game theory. Journal of Dynamics and Games, 2021  doi: 10.3934/jdg.2021030


Mirosław Lachowicz, Andrea Quartarone, Tatiana V. Ryabukha. Stability of solutions of kinetic equations corresponding to the replicator dynamics. Kinetic and Related Models, 2014, 7 (1) : 109-119. doi: 10.3934/krm.2014.7.109


Vassilis G. Papanicolaou, Kyriaki Vasilakopoulou. Similarity solutions of a multidimensional replicator dynamics integrodifferential equation. Journal of Dynamics and Games, 2016, 3 (1) : 51-74. doi: 10.3934/jdg.2016003


Jeremias Epperlein, Vladimír Švígler. On arbitrarily long periodic orbits of evolutionary games on graphs. Discrete and Continuous Dynamical Systems - B, 2018, 23 (5) : 1895-1915. doi: 10.3934/dcdsb.2018187


Mathias Staudigl, Jan-Henrik Steg. On repeated games with imperfect public monitoring: From discrete to continuous time. Journal of Dynamics and Games, 2017, 4 (1) : 1-23. doi: 10.3934/jdg.2017001


Sébastien Guisset. Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations. Kinetic and Related Models, 2020, 13 (4) : 739-758. doi: 10.3934/krm.2020025


Yannick Viossat. Game dynamics and Nash equilibria. Journal of Dynamics and Games, 2014, 1 (3) : 537-553. doi: 10.3934/jdg.2014.1.537

2020 Impact Factor: 1.327


  • PDF downloads (52)
  • HTML views (0)
  • Cited by (21)

Other articles
by authors

[Back to Top]