The question of efficiency of market organization is an important one in economics. When theoretical results suggest the dominance of auctions, empirical studies present more mitigated results putting forward that the global efficiency depends on agents' characteristics and market environment. The Boulogne s/mer fish market is organized in a particular way. Both buyers and sellers can daily choose to exchange through an auction mechanism or through a negotiated one. First empirical results reveal that, at a macro level, this organization is a stable one: the negative price-quantity relation is verified, suggesting a global rationality, even if this relation is not verified for all the individuals. At a micro-level, empirical evidence points out that the agents purchase most of the time on one same market (auctions or negotiated) and this market corresponds to the best choice for them, in terms of prices and quantities sold. A second result then suggests that the performance of a mode of organization depends on the characteristics of the traders and on the features of the good sold. Empirical study also reveals that most of the agents regularly switch from one market to the other. To understand the reasons for this switching, we consider this market as a complex system and simulate an agent based model where limited rational individuals are endowed with simple learning rules (noisy or myopic strategies). The auction sub-market plays a benchmark role, the only strategic possibility for sellers is to decide to go (or not) on the negotiated sub-market. A third result is that macro stability results from the aggregate behaviour of limited rational individuals and this, without any need of central coordinator. A fourth result is that agents daily choose their sub-market according to the global quantities sold on the whole market.