Eur. Phys. J. B 18, 159-162 (2000)
https://doi.org/10.1007/s100510070088

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

¹ Mathematics Department, Faculty of Science, Al-Ain PO Box 17551, UAE
² Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
³ Mathematics Department, Faculty of Education, El-Arish 45111, Egypt

Received: 8 July 2000
Revised: 23 July 2000
Published online: 15 November 2000

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.