Collective Helping and Bystander Effects in Coevolving Helping Networks

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We study collective helping behavior and bystander effects in a coevolving helping network model. A node and a link of the network represents an agent who renders or receives help and a friendly relation between agents, respectively. A helping trial of an agent depends on relations with other involved agents and its result (success or failure) updates the relation between the helper and the recipient. We study the network link dynamics and its steady states analytically and numerically. The full phase diagram is presented with various kinds of active and inactive phases and the nature of phase transitions are explored. We find various interesting bystander effects, consistent with the field study results, of which the underlying mechanism is proposed.