Profitability, efficiency, and inequality in double auction markets with snipers

Abstract

This research builds upon two early efforts to explore robot trading strategies within the double auction market: (1) Gode and Sunder's Zero Intelligence robots, a simple, loss-avoiding, random, persistent, liquidity-providing strategy that produced, in double auction markets, high efficiency of allocation and market price convergence (within-period) towards the predictions of competitive theory; and (2) an entirely parasitic version of Todd Kaplan's Snipers, a simple, loss-avoiding, deterministic, liquidity-removing strategy. The original version of Kaplan's Snipers achieved the highest profit in an early tournament (the Santa Fe Double Auction Tournament) in part by accepting others’ orders when there was an excellent price, a low bid-ask spread, or time was running out. As we increase the proportion of snipers in a market, we find that sniping is not generally superior to the ZI strategy and that the snipers’ parasitic and end-of-period behaviors eventually cause extreme price variance and divergence from competitive equilibrium, lower market efficiencies, and rising Gini coefficients of inequality. Our results contrast with earlier claims by Gode and Sunder and others that double auction market efficiency and convergence to competitive equilibria are market properties relatively insensitive to agent strategies. Instead, we find a need to consider agent strategy in explaining how our market outcomes differ from those previously obtained either by Gode and Sunder or by Kaplan's successful tournament entry. Specifically, the interaction of parasitic sniper strategies creates a trading constraint: snipers will never trade with each other. These strategy-induced trading constraints force the standard market efficiency metric lower as the sniper population rises.

Introduction

Does a liquidity-removing strategy affect market efficiency or fairness? We examine this question in the context of private values, double auction (henceforth DA) market simulations populated by a mix of two types of robots. Some robots execute Gode and Sunder's (1993) well-known random, loss-avoiding, Zero Intelligence (or ZI) strategy. Other robots execute a fully-parasitic version of Todd Kaplan's sniper¹ robots, another loss-avoiding strategy. The ZI robots are both liquidity providers and liquidity removers. The Kaplan-sniper-like robots wait to trade only on exceptional prices, low bid-ask spread, or near market expiration. These robots place orders only when trades would immediately result and are therefore only liquidity removers.

Our choice to focus on simple strategies derives from the success of previous research. Both Gode and Sunder (1993), and Rust et al. (1993) extoll the benefits of simplicity. The former, emphasize all the complexities missing from their ZI robots, and the latter emphasize all the complexities missing from the Kaplan robot winning their contest.

This paper is a new attempt at understanding an old but fundamental tension in markets between noisy liquidity providers (ZIs) and liquidity takers (snipers). This tension exists within the double auction literature, where there is typically no centralized or regulated market maker who is required to maintain a bid and ask for an orderly market. Bossaerts and Plott (2008) show that the dynamics of the double auction order queue, which actively demonstrates this tension between liquidity provision and removal, allows markets to solve systems of equations. This tension is also a background issue when considering market policies and interventions, e.g., in Brewer et al. (2013), and in the early research reported in the Santa Fe conference volume The Double Auction Market (Friedman 1993). In our paper, in order to produce a more generic result, we seek to understand this tension outside the usual setting of financial market modeling where agents are modeled explicitly as market makers, noisy liquidity takers, or informed traders (e.g., Glosten and Milgrom, 1985, Kyle, 1985, Wah et al., 2016).

We explore results in two double-auction market environments across many treatments and thousands of periods. We compare our simulations both against each other and against theoretical predictions based on the competitive equilibrium (henceforth CE). We use the CE as a benchmark for predicting and comparing outcomes, a common research practice across a variety of market environments, agent strategies, and special situations since Smith (1962).²

In both our market environments, the CE predictions are identical for prices and allocative efficiency but vary in terms of ex-ante distribution of profits. In Market 1, profits at CE are equal across agents, and in Market 2, profits at CE vary across agents. In each market, we generate population treatments. We start with a treatment containing 0% snipers (and 100% ZI robots) and successively increase the proportion of snipers in the DA markets to 5%, 10%, 20%, …, 90%, and finally 95% in additional treatments.

We report properties of prices, profits, allocation efficiency, and Gini coefficients. We choose Gini coefficients as a metric for evaluating market inequality or "fairness." While common in the development literature and statistical reports, this metric has also found broader application.³ Although our usage of Gini coefficients is not the first we know of in the economic simulation literature,⁴ it may be among the first in the DA literature.

The results shown here are but a small contribution towards the eventual understanding of the outcomes – efficiency, inequality, and price dispersion – that may arise in DA markets. Explorations in simple environments are part of the basic science needed to eventually understand more complex market phenomena. For example, the substantial, mostly negative media coverage of high-frequency traders (HFTs) and the “flash crash” on May 6, 2010, raised significant interest and concerns about the fairness of markets and the role of HFTs in the stability and price efficiency of markets (Brogaard et al., 2014). These concerns led the UK Government to sponsor a collection of projects on the future of regulated markets, including the Brewer et al. (2013) double auction simulations that began with uncoordinated random DA order flow and studied the potential outcomes of various market crash interventions. Our paper differs, in part, by studying DA order flow resulting from a combination of non-strategic (ZI) and strategic‑but‑unreasonable (Kaplan-like sniper) strategies. The results here add to the literature that can, from simulation data, demonstrate undesirable outcomes in a market without waiting for their costly manifestation or the complex milieu of ex-post finger pointing and justifications. In our case, it allows associating bad market outcomes with the specific behavior of a liquidity-removing strategy. These outcomes are not binary but rather involve specific patterns of change that manifest as the proportion of snipers increases and crowds out the outcomes originally dominated by ZI behavior.

The remainder of this paper is organized as follows: Section 2 introduces the market mechanism, environment, metrics, and predictions based on CE; Section 3 describes trading strategies and population treatments; Section 4 reports the results of our numerical experiments; and Section 5 concludes.