Abstract:
This paper extend a limit order book model of security trading from Goettler, et al. (2005) by adding a dark pool which does not publicly display trading orders. This model is a sequential game with risk-neutral traders. We use a stochastic algorithm followed by Pakes and McGuire (2001) to solve a Markov-perfect equilibrium as the optimal action of a trader. We find that when added a dark pool, market quality worsens (market depth declines and bid-ask spread widen), and total fill rate decreases. The deterioration of market quality in a limit order book results from an order migration to a dark pool to seek a better expected surplus as traders can save half-spread in a dark pool, but these effects are the benefit in overall welfare.
