  Loyal buyer-seller relationships can arise by design, e.g. when a seller
tailors a product to a specific market niche to accomplish the best possible
returns, and buyers respond to the dedicated efforts the seller makes to meet
their needs. We ask whether it is possible, instead, for loyalty to arise
spontaneously, and in particular as a consequence of repeated interaction and
co-adaptation among the agents in a market. We devise a stylized model of
double auction markets and adaptive traders that incorporates these features.
Traders choose where to trade (which market) and how to trade (to buy or to
sell) based on their previous experience. We find that when the typical scale
of market returns (or, at fixed scale of returns, the intensity of choice)
become higher than some threshold, the preferred state of the system is
segregated: both buyers and sellers are segmented into subgroups that are
persistently loyal to one market over another. We characterize the segregated
state analytically in the limit of large markets: it is stabilized by some
agents acting cooperatively to enable trade, and provides higher rewards than
its unsegregated counterpart both for individual traders and the population as
a whole.
