Building ethical machines may involve bestowing upon them the emotional capacity to self-evaluate and repent on their actions. While apologies represent potential strategic interactions, the explicit evolution of guilt as a behavioural trait remains poorly understood. Our study delves into the co-evolution of two forms of emotional guilt: social guilt entails a cost, requiring agents to exert efforts to understand others' internal states and behaviours; and non-social guilt, which only involves awareness of one's own state, incurs no social cost. Resorting to methods from evolutionary game theory, we study analytically, and through extensive numerical and agent-based simulations, whether and how guilt can evolve and deploy, depending on the underlying structure of the systems of agents. Our findings reveal that in lattice and scale-free networks, strategies favouring emotional guilt dominate a broader range of guilt and social costs compared to non-structured well-mixed populations, so leading to higher levels of cooperation. In structured populations, both social and non-social guilt can thrive through clustering with emotionally inclined strategies, thereby providing protection against exploiters, particularly for less costly non-social strategies. These insights shed light on the complex interplay of guilt and cooperation, enhancing our understanding of ethical artificial intelligence.

Computational simulation of evolutionary game theory interactions on networks, ran using Agents.jl in Julia. Equilibria analysis and replicator dynamics solving done using a mix of Julia and Python. Processed using various Julia data and analysis facilities (DataFrames.jl, PlotlyJS.jl, Makie.jl).

Funding provided by: UK Research and InnovationROR ID: https://ror.org/001aqnf71Award Number: MR/Z505833/1 Funding provided by: Engineering and Physical Sciences Research CouncilROR ID: https://ror.org/0439y7842Award Number: EP/Y00857X/1