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Since the depth and liquidity of a market depend on the entry decisions of all potential participants, each trader assesses them according to conjectures about entry by others. If trade is equally costly across markets, this externality leads to the concentration of trade on one market. If not, it can produce multiple conjectural equilibria, some where trade concentrates on one market and others where large traders resort to a separate market or to search for a trading partner. While fragmentation is welfare-reducing in the two-market case, no such ranking is possible if it involves off-exchange search.
Marco Pagano (Mon,) studied this question.