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behaviour of human traders interacting with GD and
ZIP robot traders, in a CDA with a Limit Order Book
(LOB: explained in more detail in Section 2.2, below),
and demonstrated that both GD and ZIP reliably
outperformed human traders. Neither GD nor ZIP had
been designed to work with the LOB, so the IBM team
modified both strategies for their study. A follow-on
2001 paper by Tesauro and Das (two co-authors of the
IBM IJCAI paper) described a more extensively
Modified GD (MGD) strategy, and later Tesauro and
Bredin (2002) described the GD eXtended (GDX)
strategy. Both MGD and GDX were each claimed to
be the strongest-known public-domain trading
strategies at the times of their publication.
Subsequently, Vytelingum’s 2006 thesis
introduced the Adaptive Aggressive (AA) strategy
which, in an AIJ paper (Vytelingum et al., 2007), and
in later ICAART and IJCAI papers (De Luca and Cliff
2012a, 2012b), was shown to be dominant over ZIP,
GDX, and human traders. Thus far then, AA holds the
title.
However Vach (2015) recently presented results
from experiments with the OpEx market simulator (De
Luca, 2015), in which AA, GDX, and ZIP were set to
compete against one another, and in which the
dominance of AA is questioned: Vach’s results
indicate that whether AA dominates or not can be
dependent on the ratio of AA:GDX:ZIP in the
experiment: for some ratios, Vach found AA to
dominate; for other ratios, it was GDX. Vach studied
only a relatively small sample from the space of
possible ratios, but his results prompted the work
reported here, in which we exhaustively sample a wide
range of differing ratios of four trading strategies (AA,
ZIC, ZIP, and the minimally simple SHVR strategy
described in Section 2.2), doing a brute-force search
for situations in which AA is outperformed by the other
strategies. The combinatorics of such a search are quite
explosive, and in Section 5 we report on results from
over 3.4 million individual simulations of market
sessions. Our findings indicate that Vach’s observation
was correct: AA’s dominance depends on how many
other AA traders are in the market; and, in aggregate,
AA is routinely outperformed by ZIP and by SHVR.
2.2 On Laboratory Models of Markets
Smith’s early experiments were laboratory models of
so called open-outcry trading pits, a common sight in
any real financial exchange before the arrival of
electronic trader-terminals in the 1970s. In a trading
pit, human traders huddle together and shout out their
bids and offers, and also announce their willingness to
accept a counterparty’s most recent shout. It’s a chaotic
scene, now largely consigned to the history books. In
the closing quarter of the 20
th
Century, traders moved
en masse to interacting with each other instead via
electronic means: traders “shouted” their offer or bids
or acceptances by typing orders on keyboards and then
sending those orders to a central server that would
display an aggregate summary of all orders currently
“shouted” onto the market. That aggregate summary is
very often in the form of a Limit Order Book or LOB:
the LOB shows a summary of all bids and offers
currently live in the market. At its simplest, the LOB is
a table of numbers, divided into the bid side and the ask
side (also known as the offer side). Both sides of the
LOB show the best price at the top, with less good
prices arranged below in numeric order of price: for the
bid side this means the highest-priced bid at the top
with the remaining bid prices displayed in descending
order below; and for the ask side the lowest-priced
offer is at the top, with the remaining offers arranged
in ascending order below. The arithmetic mean of the
best bid and best ask prices is known as the mid-price,
and their difference is the spread. For each side of the
LOB, at each price on the LOB, the quantity available
on that side at that price is also indicated, but with no
indication of who the relevant orders came from: in this
sense the LOB serves not only to aggregate all
currently live orders, but also to anonymize them.
Traders in LOB-based markets can usually cancel
existing orders to delete them from the LOB. In a
common simple implementation of a LOB, traders can
accept the current best bid or best offer by issuing a
quote that crosses the spread: i.e., by issuing an order
that, if added to the LOB, would result in the best bid
being at a higher price than the best ask. Rather than be
added to the LOB, if a bid order crosses the spread then
it is matched with the best offer on the ask side (known
as lifting the ask), whereas an ask that crosses the
spread is matched with the best bid (hitting the bid);
and in either case a transaction then occurs between the
trader that had posted the best price on the relevant side
of the LOB, and the trader that crossed the spread. The
price of the resulting transaction is whatever price was
hit or lifted from the top of the LOB.
Smith’s earliest experiments pre-dated the arrival
of electronic trading in real financial markets, and so
they can be thought of as laboratory models of open-
outcry trading pits. Even though the much later work
by Gode and Sunder, Cliff, Gjerstad and Dickhaut, and
Vytelingum all came long after the introduction of
electronic LOBs in real markets, these academic
studies all stuck with Smith’s original methodology, of
modelling open-outcry markets (often by essentially
operating a LOB with the depth fixed at 1, so the only
information available to traders is the current best, or
Exhaustive Testing of Trader-agents in Realistically Dynamic Continuous Double Auction Markets: AA Does Not Dominate
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