Dynamics of helping behavior and networks in a small world

To investigate an effect of social interaction on the bystanders' intervention in emergency situations a rescue model was introduced which includes the effects of the victim's acquaintance with bystanders and those among bystanders from a network perspective. This model reproduces the experimental result that the helping rate (success rate in our model) tends to decrease although the number of bystanders k increases. And the interaction among homogeneous bystanders results in the emergence of hubs in a helping network. For more realistic consideration it is assumed that the agents are located on a one-dimensional lattice (ring), then the randomness p[0,1] is introduced: the kp random bystanders are randomly chosen from a whole population and the k-kp near bystanders are chosen in the nearest order to the victim. We find that there appears another peak of the network density in the vicinity of k=9 and p=0.3 due to the cooperative and competitive interaction between the near and random bystanders.