Agent-based dynamics of criminal propensity
The Retribution and Reciprocity Model (RRM) is a novel framework presented in evolutionary criminology to understand causes of crime through the lens of cooperation. We formalise RRM as an agent-based dynamical system in which criminal propensity evolves through pairwise interactions and through observations of others' interactions. The mathematical model extends bounded confidence opinion dynamics with two novel features: an agent-specific attractor representing the perception of the environment, and the participation of third-party witnesses. We prove that individual propensities remain bounded and establish sufficient conditions for convergence to an extreme value and to the agent's perception of the environment. Simulations show that the dominant system behaviour is not convergence but persistent oscillations, a rare phenomenon in bounded confidence models arising here without the adaptive confidence bounds through which it has previously been obtained. We derive a necessary condition for oscillations, and find that a population sharing a uniform but neutral perception of the environment tends to polarise to the extremes, while a uniform non-neutral perception tends to yield consensus. The polarising regime is confined to a narrow band of near-neutral perceptions, whose width decreases with population size and increases with the strength of reciprocal and retributive tendencies.