Social manifestation of guilt leads to stable cooperation in multi-agent systems

Inspired by psychological and evolutionary studies, we present here theoretical models wherein agents have the potential to express guilt with the ambition to study the role of this emotion in the promotion of pro-social behaviour. To achieve this goal, analytical and numerical methods from evolutionary game theory are employed to identify the conditions for which enhanced cooperation emerges within the context of the iterated prisoners dilemma. Guilt is modelled explicitly as two features, i.e. A counter that keeps track of the number of transgressions and a threshold that dictates when alleviation (through for instance apology and self-punishment) is required for an emotional agent. Such an alleviation introduces an effect on the payoff of the agent experiencing guilt. We show that when the system consists of agents that resolve their guilt without considering the co-player's attitude towards guilt alleviation then cooperation does not emerge. In that case those guilt prone agents are easily dominated by agents expressing no guilt or having no incentive to alleviate the guilt they experience. When, on the other hand, the guilt prone focal agent requires that guilt only needs to be alleviated when guilt alleviation is also manifested by a defecting co-player, then cooperation may thrive. This observation remains consistent for a generalised model as is discussed in this article. In summary, our analysis provides important insights into the design of multi-agent and cognitive agent systems where the inclusion of guilt modelling can improve agents' cooperative behaviour and overall benefit.