Cooperation dynamics of reputation-based manhattan distance social circle in spatial prisoner's dilemma game in evolutionary game theory

Inspired by the complex interplay between reputation and social proximity, we propose a novel model called the Manhattan distance reputation circle, integrating nonlinear reputation mechanisms and interaction range within the spatial prisoner's dilemma game. In this model, the average reputation of neighbors sharing the same strategy within a specific Manhattan distance is incorporated into the central node's strategy update rule. Two rules are introduced to evaluate average reputation: rule A employs the standard averaging method, while rule B applies a distance-based decay, introducing a nonlinear weighting to the reputation, giving more influence to closer neighbors. Monte Carlo simulations reveal that the proposed model exhibits nonlinear dynamics that promote the emergence of cooperative strategies. Specifically, greater interaction range and reputation adjustment values enhance cooperation, although the impact of interaction range plateaus beyond a certain threshold. While both rules foster cooperation, rule B's nonlinear reputation decay reduces the fluctuations in cooperation seen in rule A as alpha increases under high introduction rates in the model.