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]

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

Saul Mendoza-Palacios, Onésimo Hernández-Lerma. Stability of the replicator dynamics for games in metric spaces. Journal of Dynamics & Games, 2017, 4 (4) : 319-333. doi: 10.3934/jdg.2017017
[3]

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

Anna Lisa Amadori, Astridh Boccabella, Roberto Natalini. A hyperbolic model of spatial evolutionary game theory. Communications on Pure & Applied Analysis, 2012, 11 (3) : 981-1002. doi: 10.3934/cpaa.2012.11.981
[5]

Eduardo Espinosa-Avila, Pablo Padilla Longoria, Francisco Hernández-Quiroz. Game theory and dynamic programming in alternate games. Journal of Dynamics & Games, 2017, 4 (3) : 205-216. doi: 10.3934/jdg.2017013
[6]

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
[7]

William H. Sandholm. Local stability of strict equilibria under evolutionary game dynamics. Journal of Dynamics & Games, 2014, 1 (3) : 485-495. doi: 10.3934/jdg.2014.1.485
[8]

Jeremias Epperlein, Stefan Siegmund, Petr Stehlík, Vladimír  Švígler. Coexistence equilibria of evolutionary games on graphs under deterministic imitation dynamics. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 803-813. doi: 10.3934/dcdsb.2016.21.803
[9]

Sylvain Sorin. Replicator dynamics: Old and new. Journal of Dynamics & Games, 2020, 7 (4) : 365-386. doi: 10.3934/jdg.2020028
[10]

King-Yeung Lam. Dirac-concentrations in an integro-pde model from evolutionary game theory. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 737-754. doi: 10.3934/dcdsb.2018205
[11]

Hassan Najafi Alishah, Pedro Duarte. Hamiltonian evolutionary games. Journal of Dynamics & Games, 2015, 2 (1) : 33-49. doi: 10.3934/jdg.2015.2.33
[12]

Lianju Sun, Ziyou Gao, Yiju Wang. A Stackelberg game management model of the urban public transport. Journal of Industrial & Management Optimization, 2012, 8 (2) : 507-520. doi: 10.3934/jimo.2012.8.507
[13]

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
[14]

Mirosław Lachowicz, Andrea Quartarone, Tatiana V. Ryabukha. Stability of solutions of kinetic equations corresponding to the replicator dynamics. Kinetic & Related Models, 2014, 7 (1) : 109-119. doi: 10.3934/krm.2014.7.109
[15]

Vassilis G. Papanicolaou, Kyriaki Vasilakopoulou. Similarity solutions of a multidimensional replicator dynamics integrodifferential equation. Journal of Dynamics & Games, 2016, 3 (1) : 51-74. doi: 10.3934/jdg.2016003
[16]

Jeremias Epperlein, Vladimír Švígler. On arbitrarily long periodic orbits of evolutionary games on graphs. Discrete & Continuous Dynamical Systems - B, 2018, 23 (5) : 1895-1915. doi: 10.3934/dcdsb.2018187
[17]

Mathias Staudigl, Jan-Henrik Steg. On repeated games with imperfect public monitoring: From discrete to continuous time. Journal of Dynamics & Games, 2017, 4 (1) : 1-23. doi: 10.3934/jdg.2017001
[18]

Sébastien Guisset. Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations. Kinetic & Related Models, 2020, 13 (4) : 739-758. doi: 10.3934/krm.2020025
[19]

Yannick Viossat. Game dynamics and Nash equilibria. Journal of Dynamics & Games, 2014, 1 (3) : 537-553. doi: 10.3934/jdg.2014.1.537
[20]

Scott G. McCalla. Paladins as predators: Invasive waves in a spatial evolutionary adversarial game. Discrete & Continuous Dynamical Systems - B, 2014, 19 (5) : 1437-1457. doi: 10.3934/dcdsb.2014.19.1437

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (39)
  • HTML views (0)
  • Cited by (21)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences