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

Market fragmentation and market consolidation: Multiple steady states in systems of adaptive traders choosing where to trade