“Friends Are Thieves of Time”: Heuristic attention sharing in stable friendship networks

Abstract

This paper studies a model of network formation in which agents create links following a simple heuristic — they invest their limited resources proportionally more in neighbours who have fewer links. This decision rule captures the notion that when considering social value more connected agents are on average less beneficial as neighbours and node degree is a useful proxy when payoffs are difficult to compute. The decision rule illustrates an externalities effect whereby an agent’s actions also influence his neighbours’ neighbours. Besides complete networks and fragmented networks with complete components, the pairwise stable networks produced by this model include many non-standard ones with characteristics observed in real life networks like clustering and irregular components. Multiple stable states can develop from the same initial structure — the stable networks could have cliques linked by intermediary agents while sometimes they have a core–periphery structure. The observed pairwise stable networks have close to optimal welfare. This limited loss of welfare is due to the fact that when a link is established, this is beneficial to the linking agents, but makes them less attractive as neighbours for others, thereby partially internalising the externalities the new connection has generated.