Journal of Mathematical Biology

, Volume 68, Issue 1–2, pp 181–206 | Cite as

Reaction networks and evolutionary game theory

  • Tomas Veloz
  • Pablo Razeto-Barry
  • Peter Dittrich
  • Alejandro Fajardo


The powerful mathematical tools developed for the study of large scale reaction networks have given rise to applications of this framework beyond the scope of biochemistry. Recently, reaction networks have been suggested as an alternative way to model social phenomena. In this “socio-chemical metaphor” molecular species play the role of agents’ decisions and their outcomes, and chemical reactions play the role of interactions among these decisions. From here, it is possible to study the dynamical properties of social systems using standard tools of biochemical modelling. In this work we show how to use reaction networks to model systems that are usually studied via evolutionary game theory. We first illustrate our framework by modeling the repeated prisoners’ dilemma. The model is built from the payoff matrix together with assumptions of the agents’ memory and recognizability capacities. The model provides consistent results concerning the performance of the agents, and allows for the examination of the steady states of the system in a simple manner. We further develop a model considering the interaction among Tit for Tat and Defector agents. We produce analytical results concerning the performance of the strategies in different situations of agents’ memory and recognizability. This approach unites two important theories and may produce new insights in classical problems such as the evolution of cooperation in large scale systems.


Reaction networks Evolutionary game theory Cooperation  Tit for Tat 

Mathematics Subject Classification (2000)

91A22 91A13 92B 93D20 37F15 



We would like to thanks the Grupo de Sociología Computacional y Modelamiento en Ciencias Sociales, Instituto de Filosofía y Ciencias de la Complejidad (IFICC), for useful suggestions for this paper, and to our anonymous reviewer for the extremely useful comments on the content and presentation of the paper.

Supplementary material

285_2012_626_MOESM1_ESM.pdf (82 kb)
Supplementary material (PDF 82KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tomas Veloz
    • 1
    • 2
  • Pablo Razeto-Barry
    • 2
    • 3
  • Peter Dittrich
    • 4
  • Alejandro Fajardo
    • 5
  1. 1.Mathematics DepartmentUniversity of British ColumbiaKelownaCanada
  2. 2.Instituto de Filosofía y Ciencias de la Complejidad IFICCSantiagoChile
  3. 3.Universidad Diego Portales, Vicerrectoría AcadémicaSantiagoChile
  4. 4.Friedrich-Schiller-University Jena, Institute of Computer Science Bio Systems Analysis GroupJenaGermany
  5. 5.Departamento de BiologíaUniversidad de los AndesBogotáColombia

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