To snipe or not to snipe, that is the question! Transitions in sniping behaviour among competing algorithmic traders

Abstract

In this paper we extend the investigation into the transition from sure to probabilistic sniping as introduced in Menkveld and Zoican \cite{mz2017}. In that paper, the authors introduce a stylized version of a competitive game in which high frequency traders (HFTs) interact with each other and liquidity traders. The authors then show that risk aversion plays an important role in the transition from sure to mixed (or probabilistic) sniping. In this paper, we re-interpret and extend these conclusions in the context of repeated games and highlight some differences in results. In particular, we identify situations in which probabilistic sniping is genuinely profitable that are qualitatively different from the ones obtained in \cite{mz2017}. It turns out that beyond a specific risk aversion threshold the game resembles the well-known prisoner's dilemma, in that probabilistic sniping becomes a way to cooperate among the HFTs that leaves all the participants better off. In order to turn this into a viable strategy for the repeated game, we show how compliance can be monitored through the use of sequential statistical testing. Keywords: algorithmic trading, bandits, high-frequency exchange, Nash equilibrium, repeated games, sniping, subgame-perfect equilibrium, Sequential probability ratio, transition