Indirect Reciprocity with Environmental Feedback

TL;DR

This paper introduces a co-evolutionary framework coupling moral assessment, strategy updating, and environmental dynamics, showing how environmental feedback promotes cooperation and influences social norms in complex systems.

Contribution

It develops a novel dynamic model integrating environmental feedback into indirect reciprocity, revealing how it facilitates cooperation and affects norm effectiveness.

Findings

Environmental feedback lowers cooperation thresholds.

Strict norms are essential for resilience in dynamic environments.

Co-evolutionary dynamics promote stable high cooperation.

Abstract

Indirect reciprocity maintains cooperation in stranger societies by mapping individual behaviors onto reputation signals via social norms. Existing theoretical frameworks assume static environments with constant resources and fixed payoff structures. However, in real-world systems, individuals' strategic behaviors not only shape their reputation but also induce collective-level resource changes in ecological, economic, or other external environments, which in turn reshape the incentives governing future individual actions. To overcome this limitation, we establish a co-evolutionary framework that couples moral assessment, strategy updating, and environmental dynamics, allowing the payoff structure to dynamically adjust in response to the ecological consequences of collective actions. We find that this environmental feedback mechanism helps lower the threshold for the emergence of cooperation, enabling the system to spontaneously transition from a low-cooperation state to a stable high-cooperation regime, thereby reducing the dependence on specific initial conditions. Furthermore, while lenient norms demonstrate adaptability in static environments, norms with strict discrimination are shown to be crucial for curbing opportunism and maintaining evolutionary resilience in dynamic settings. Our results reveal the evolutionary dynamics of coupled systems involving reputation institutions and environmental constraints, offering a new theoretical perspective for understanding collective cooperation and social governance in complex environments.