Is the Electronic Open-Limit Order Book Inevitable?
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Under fairly general conditions, the article derives the equilibrium price schedule determined by the bids and offers in an open limit order book. The analysis shows: (1) the order book has a small-trade positive bid-ask spread, and limit orders profit from small trades; (2) the electronic exchange provides as much liquidity as possible in extreme situations; (3) the limit order book does not invite competition from third market dealers, while other trading institutions do; (4) If an entering exchange earns nonnegative trading profits, the consolidated price schedule matches the limit order book price schedule.
Source: Journal of Finance
Glosten, Lawrence. "Is the Electronic Open-Limit Order Book Inevitable?" Journal of Finance 49, no. 4 (September 1994): 1127-61.