This article analyses the determinants of loyalty on a market for perishable goods, where there exists no label or quality signal and quantities can be scarce. This daily market exhibits a specific bi-organization. Every morning, agents can choose between bidding or exchanging through bilateral transactions. Surprisingly, this organization is a stable one and it sounds like an economic paradox. Our hypothesis is that agents behave in a different way according to their level of information, trust or reputation. It is well accepted in economy that trust plays an important role in transactions but its definition and measurement stay, as far as we know, very elusive. This article provide a measurement of loyalty, based on the dynamics of agents' encounters. It brings into the light that, when the transaction links on the auction market reflects the economic constraints of the partners, the network of relationships on the bilateral market depends on something more. Our results help to understand the distinctive characteristics and functioning of each sub-market. This discussion contributes to the debate about the efficiency of market structures.