Simple norms facilitate consensus: Cooperation in network-based limited gossip model with multiple social norms

Indirect reciprocity sustaining large-scale human cooperation relies upon reputation consensus grounded in social norms. Whilst unified social norms may foster consensus, real-world communities often feature coexisting diverse norms — such as in multi-ethnic neighbourhoods and multicultural settings where individuals frequently judge others’ reputations by differing standards. Particularly when reputations are privately assessed and disseminated through limited gossip within structured groups, resulting evaluative divergence may exacerbate group polarisation, thereby threatening cooperative stability. To address this, this study constructs a two-layer network model with limited gossip propagation and donation games, wherein individuals’ reputations are judged according to differing norms, and gossip propagates along social network edges with finite reach. Results indicate that punitive norms readily induce group opinion polarisation and oscillatory shifts in reputation matrices under information scarcity, whereas introducing relatively simple norms fosters stable cooperation. Furthermore, we distinguish how gossip carriers – transmitting either reputation or behavioural information about focal individuals – amplify opinion divergence, finding that behavioural information propagation undermines indirect reciprocity mechanisms. Finally, results show that network segregation can help build local consensus and rescue cooperation when gossip propagation is infrequent, as modelled in segregated networks constructed via Markov Chain Monte Carlo sampling of bilateral exchanges. This study provides insights into indirect reciprocity mechanisms within structured societies featuring heterogeneous norms and constrained information propagation, aiding explanations for the coexistence of polarisation and cooperation in the real world.