This paper provides a formal definition of emergence, operative in multi-agent framework and which make sense from both a cognitive and an economics point of view. The first part discuses the ontological and epistemic dimension of emergence and provides a complementary set of definitions. Following Bonabeau, Dessalles, emergence is defined as an unexpected decrease in relative algorithmic complexity. The relative algorithmic complexity of a system measures the complexity of the shortest description that a given observer can give of the system, relative to the description tools available to that observer. Emergence occurs when RAC abruptly drops by a significant amount, i.e. the system appears much simpler than anticipated. Following Muller, we call strong emergence a situation in which the agents involved in the emerging phenomenon are able to perceive it. Strong emergence is particularly important in economic modelling, because the behaviour of agents may be recursively influenced by their perception of emerging properties. Emerging phenomena in a population of agents are expected to be richer and more complex when agents have enough cognitive abilities to perceive the emergent patterns. Our aim here is to design a minimal setting in which this kind of “strong emergence†unambiguously takes place. In part II, we design a model for strong emergence as an extension of Axtell et al. In the basic model, agents tend to correlate their fellows’ behaviour with fortuitous visible but meaningless characteristics. On some occasions, these fortuitous tags turn out to be reliable indicators of dominant and submissive behaviour in an iterative Nash bargaining tournament. One limit of this model is that dominant and submissive classes remain implicit within the system. As a consequence, classes only emerge in the eye of external observers. In the enhanced model, Individuals may deliberately choose to display a tag after observing that they are regularly dominated by other agents who display that tag. Tag display is constrained by the fact that displaying agents must endure a cost. Agents get an explicit representation of the dominant class whenever that class emerges, thus implementing strong emergence. This phenomenon results from a double-level emergence. As in the initial model, dominant and submissive strategies may emerge through amplification of fortuitous differences in agents’ personal experiences. We add the possibility of a second level in emergence, where a tag is explicitly used by agents to announce their intention to adopt a dominant strategy. Costly signalling (Spence, Zahavi et al. Gintis, Smith, Bowles) is an essential feature of this extended model. Qualities are not objective, but correspond to an emerging de facto ranking of individuals. Without strong emergence, endogenous signalling allows possible inversion in the class regime, while with strong emergence class behaviour may became a stochastically stable regim
