Emergence in multi-agent systems, part II: Axtell, Epstein and Young's revisited

The present paper discusses implications for Agent-based Computational Economics (ACE) of a formal definition of emergence introduced by Dessalles, Phan in part I of this work. This exemplification is based on an extension of the model of emergence of classes by Axtell et al. The present paper is an attempt to integrate both downward and upward causation in one single framework, in which the whole is the result of the collective interactions between agents, but, in which the agents are constrained by the whole (downward causation), by way of the social dimension of their belief (imergence). One limit of the basic model is that dominant and submissive classes remain implicit: classes only emerge for external observers (weak emergence). We enhance the model to allow for strong emergence: agents get an explicit representation of the dominant class whenever that class emerges. While with strong emergence class behaviour may became a stochastically stable regime