High Frequency Fairness

The emergence of high frequency trading has resulted in ‘bursts’ of orders arriving at an exchange (nearly) simultaneously, yet most electronic financial exchanges im- plement the continuous limit order book which requires processing of orders serially. Contrary to an assumption that appears throughout the economics literature, the tech- nology that performs serialization provides only constrained random serial dictatorship (RSD) in the sense that not all priority orderings of agents are possible. We provide necessary and sufficient conditions for fairness under different market conditions on orders for constrained RSD mechanisms. Our results show that exchanges relying on the current serialization technology cannot ensure fairness, including exchanges using ‘speed bumps.’ We find that specific forms of constrained RSD ensure fairness under certain assumptions about the content of those orders but that the general case nev- ertheless requires unconstrained RSD. Our results have implications for the design of trading exchanges.