Dynamics of helping behavior and networks

Abstract

Complex systems are usually composed of many interacting elements and show the emergent properties which arise out of elements and yet are irreducible with respect to them but explicable by means of interaction among elements. Based on this idea, by applying the statistical physics and mathematical tools to figure out social phenomena we build a dynamical agent-based model coevolving with the network structure, where each node represents each agent and the link does interaction between two agents. To investigate an effect of social interaction on the bystanders\`` intervention in emergency situations we introduce a rescue model which includes the effects of the victim\``s acquaintance with bystanders and those among bystanders from a network perspective. This model reproduces the surprising experimental result that the helping rate tends to decrease although the number of bystanders $k$ increases. Instead of the helping rate defined in the experimental studies we define the network density and success rate as observables. By the analytic approach and numerical simulations we find that the interaction among bystanders plays the most important role in both positive and negative aspects. Due to the interaction two transition points $k_1$ and $k_2$ appear, near the $k_1$ the time series of network density show the punctuated-equilibrium type behavior. 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 $p \\in [0,1]$ 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 ra...