Evolution of cooperation in indirect reciprocity: A network-based gossip model with local observation and limited propagation

The role of indirect reciprocity in sustaining cooperation stems from individuals’ strategic investment in establishing a favourable reputation. Gossip contributes to the construction of reputational mechanisms that are universally agreed upon. However, past gossip models typically assumed (1) the game process is observed by an arbitrary third party, (2) gossip propagation is random and infinite. In reality, individuals can typically only observe the actions of those they know personally, and gossip propagation is influenced by social relationships, often ceasing as the social distance from the focal individual increases. These real-world factors underscore the necessity of considering population structure, while limited observation and gossip propagation also raise concerns about the potential failure to achieve reputational consensus. To address this, we propose a network-based gossip model with local observation and limited propagation. Here, an individual’s behaviour is observable only to neighbours connected by direct edges, while their reputation propagates along the edges of the social network, constrained by social distance. We examine how factors such as the benefit-to-cost ratio of cooperation, gossip propagation frequency, network structure, error rates, and social norms influence group cooperation levels and opinion consistency. Our findings reveal the detrimental effect of restricted gossip propagation on indirect reciprocity efficacy, the pivotal role of social structure in achieving reputational consensus, and the key insight that reward-based social norms can counteract limited consensus.