We model a public limit order book (PLB) with rational investors choosing to supply or demand liquidity. Following a reduction in the tick size the effects on PLB's market quality depend on the liquidity of the stocks. Spread improves for tick-constrained stocks and deteriorates for...

We show that when a continuous dark pool is added to a limit order book that opens illiquid, book and consolidated fill rates and volume increase, but spread widens, depth declines and welfare deteriorates. The adverse effects on market quality and welfare are mitigated when book-liquidity...

We model an order book with liquidity rebates (make fees) and trading fees (take fees) that faces intermarket competition, and use the models insights to explain changes in market quality and market shares following changes in make-take fees. As predicted by our model, we document that fee...