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On coordination and continuous hawk-dove games on small-world networks

  • E. Ahmed
  • A.S. Elgazzar

Abstract:

It is argued that small-world networks are more suitable than ordinary graphs in modelling the diffusion of a concept (e.g. a technology, a disease, a tradition, ...). The coordination game with two strategies is studied on small-world networks, and it is shown that the time needed for a concept to dominate almost all of the network is of order \(\), where N is the number of vertices. This result is different from regular graphs and from a result obtained by Young. The reason for the difference is explained. Continuous hawk-dove game is defined and a corresponding dynamical system is derived. Its steady state and stability are studied. Replicator dynamics for continuous hawk-dove game is derived without the concept of population. The resulting finite difference equation is studied. Finally continuous hawk-dove is simulated on small-world networks using Nash updating rule. The system is 2-cyclic for all the studied range.

PACS. 64.60.-i General studies of phase transitions 

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Copyright information

© EDP Sciences, Springer-Verlag, Società Italiana di Fisica 2000

Authors and Affiliations

  • E. Ahmed
    • 1
  • A.S. Elgazzar
    • 2
  1. 1.Mathematics Department, Faculty of Science, Al-Ain PO Box 17551, UAE
  2. 2.Mathematics Department, Faculty of Education, El-Arish 45111, EgyptEG

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