Prosperity is associated with instability in dynamical networks

Abstract

Social, biological and economic networks grow and decline with occasional fragmentation and re-formation, often explained in terms of external perturbations. We show that these phenomena can be a direct consequence of simple imitation and internal conflicts between ‘cooperators’ and ‘defectors’. We employ a game-theoretic model of dynamic network formation where successful individuals are more likely to be imitated by newcomers who adopt their strategies and copy their social network. We find that, despite using the same mechanism, cooperators promote well-connected highly prosperous networks and defectors cause the network to fragment and lose its prosperity; defectors are unable to maintain the highly connected networks they invade. Once the network is fragmented it can be reconstructed by a new invasion of cooperators, leading to the cycle of formation and fragmentation seen, for example, in bacterial communities and socio-economic networks. In this endless struggle between cooperators and defectors we observe that cooperation leads to prosperity, but prosperity is associated with instability. Cooperation is prosperous when the network has frequent formation and fragmentation.

Assortativity Evolving from Social Dilemmas

“…For example, when interactions are spatial, then individuals' choices to relocate would determine evolving assortativity through dynamical networks. Importantly, we note that dynamical networks may lead to the re-scaling of payoffs, as reported by Pacheco et al (2006a,b), to instability, as reported by Cavaliere et al (2012), as well as to the emergence of multilevel selection and strong heterogeneities, as reported by Szolnoki and Perc (2009) and Szolnoki et al (2008). This surely has implications for local assortativity and voting procedures (which may no longer be global) and is an interesting aspect that deserves attention in future research.…”

Indirect reciprocity with optional interactions

“…If you end or do not begin an interaction, because a player has defected against someone else, then this is a form of indirect reciprocity (Fu et al, 2008). Likewise it is a form of indirect reciprocity if you preferentially seek interactions with people who have cooperated with others (Tarnita et al, 2009;Du and Fu, 2011;Cavaliere et al, 2012). Optional interactions and ostracism have also been discussed in the context of multi-player games such as the public goods game or common pool resource games (Aktipis, 2004;Chiang, 2008;Nakamura and Masuda, 2012;Tavoni et al, 2012;Lade et al, 2013).…”

Expectations of Fairness and Trust Co-Evolve in Environments of Partial Information

“…3. This kind of highly cooperative, but unstable dynamic is often witnessed in the evolution of cooperation literature [22,36].…”