Frequent batch auction versus continuous time auction under order cancellation and maker-taker fee

We investigate the consequences of different market designs and policies on market quality in a high-frequency market. Based on an extensible theoretical framework, high-frequency traders in our model can be either market makers or arbitragers, which leads to a Nash equilibrium between their utilities. We consider the optimal strategies of different market agents in various market conditions based on the equilibrium. We find frequent batch auctions benefit market liquidity but harm market volatility compared to continuous-time auctions. Order cancellation ban harms market quality while the taker fee is beneficial. We also find that market design and policy changes are only effective in low-latency markets. Finally, we address that the total effect of high-frequency trading is positive, so it is vital to reap high-frequency traders' benefits while minimising their harms in high-frequency markets.