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

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