Building ethical machines may involve bestowing upon them the emotional capacity to self-evaluate and repent on their actions. While reparative measures, such as apologies, are often considered as possible strategic interactions, the explicit evolution of the emotion of guilt as a behavioural phenotype is not yet well understood. Here, we study the co-evolution of social and non-social guilt of homogeneous or heterogeneous populations, including well-mixed, lattice and scale-free networks. Socially aware guilt comes at a cost, as it requires agents to make demanding efforts to observe and understand the internal state and behaviour of others, while non-social guilt only requires the awareness of the agents' own state and hence incurs no social cost. Those choosing to be non-social are however more sensitive to exploitation by other agents due to their social unawareness. Resorting to methods from evolutionary game theory, we study analytically, and through extensive numerical and agent-based simulations, whether and how such social and non-social guilt can evolve and deploy, depending on the underlying structure of the populations, or systems, of agents. The results show that, in both lattice and scale-free networks, emotional guilt prone strategies are dominant for a larger range of the guilt and social costs incurred, compared to the well-mixed population setting, leading therefore to significantly higher levels of cooperation for a wider range of the costs. In structured population settings, both social and non-social guilt can evolve and deploy through clustering with emotional prone strategies, allowing them to be protected from exploiters, especially in case of non-social (less costly) strategies. Overall, our findings provide important insights into the design and engineering of self-organised and distributed cooperative multi-agent systems.

翻译：构建伦理机器可能涉及赋予其自我评估和悔过行为的情绪能力。尽管道歉等补救措施常被视为可能的策略性互动，但内疚情绪作为行为表型的明确演化机制尚不明确。本文研究了同质或异质群体（包括混合群体、晶格网络和无标度网络）中社会性与非社会性内疚的协同演化。具有社会意识的内疚需要代理付出代价——它们必须耗费精力观察并理解他人的内在状态与行为；而非社会性内疚仅需代理觉察自身状态，因此不产生社会成本。然而，选择非社会性策略的代理因缺乏社会意识而更易被他者利用。借助演化博弈论方法，我们通过理论分析、大规模数值模拟及基于代理的仿真，研究了社会性与非社会性内疚在不同群体（或系统）结构下的演化与传播机制。结果表明：在晶格网络和无标度网络中，相较于混合群体环境，内疚倾向策略在更宽泛的愧疚成本与社会成本区间内占据主导地位，从而在更大成本范围内显著提升合作水平。在结构化群体中，社会性与非社会性内疚均可通过内疚倾向策略的聚类实现演化与扩散——这种聚类机制可保护策略免受剥削者侵害，尤其对非社会性（低成本）策略效果显著。总体而言，本研究为自组织分布式协作多代理系统的设计与工程化提供了重要启示。