  Technological progress is leading to proliferation and diversification of
trading venues, thus increasing the relevance of the long-standing question of
market fragmentation versus consolidation. To address this issue
quantitatively, we analyse systems of adaptive traders that choose where to
trade based on their previous experience. We demonstrate that only based on
aggregate parameters about trading venues, such as the demand to supply ratio,
we can assess whether a population of traders will prefer fragmentation or
specialization towards a single venue. We investigate what conditions lead to
market fragmentation for populations with a long memory and analyse the
stability and other properties of both fragmented and consolidated steady
states. Finally we investigate the dynamics of populations with finite memory;
when this memory is long the true long-time steady states are consolidated but
fragmented states are strongly metastable, dominating the behaviour out to long
times.
