Dynamic limit order market with diversity in trading horizons

This paper considers a trading game in which sequentially arriving liquidity traders either opt for a market order or for a limit order. One class of traders is considered to have an extended trading horizon, implying their impatience is linked to their trading orientation. More specifically, sellers are considered to have a trading horizon of two periods, whereas buyers only have a single-period trading scope (the extended buyer-horizon case is completely symmetric). Clearly, as the life span of their submitted limit orders is longer, this setting implies sellers are granted a natural advantage in supplying liquidity. This benefit is hampered, however, by the direct competition arising between consecutively arriving sellers. Closed-form characterizations for the order submission strategies are obtained when solving for the equilibrium of this dynamic game. These allow to examine how these forces affect traders' order placement decisions. Further, the analysis yields insight into the dynamic process of price formation and into the market clearing process of a non-intermediated, order driven market.