Effects of price signal choices on market stability

Journal of Economic Behavior & Organization
Vol. 52 (2003) 235–251
Effects of price signal choices on market stability
Hideyuki Mizuta a,?, Ken Steiglitz b, Erez Lirov b
a Tokyo Research Laboratory, IBM Japan, 1623-14 Shimotsuruma, Yamato, Kanagawa 242-8502, Japan
b Computer Science Department, Princeton University, 35 Older Street, Princeton, NJ, USA
Received 9 April 2001; received in revised form 27 December 2001; accepted 7 May 2002
Abstract
Using simulation and analysis we show that agent-based auction-cleared automated markets can
be stabilized using only completely myopic agents (without value traders), if these na¨?ve agents are
provided with a price signal that re?ects order book information. This demonstrates that information
in the order book is extremely valuable, that prediction can be replaced by better instantaneous
information about others’ bids, and suggests new, more stable algorithms for market-based control.
© 2003 Elsevier Science B.V. All rights reserved.
JEL classi?cation: C60; E30; E37
Keywords: Automated markets; Myopic agents; Price signal; Agent-based simulation
1. Introduction
1.1. The problem of market stability
The stability of prices in asset markets is clearly a central issue in economics. From a
systems point of view markets inevitably entail the feedback of information in the form of
price signals and, like all feedback systems, may exhibit unstable behavior. Under varying
circumstances we might expect convergence to some fundamental value, more or less regular
oscillations, chaotic oscillations, sharp rises or falls followed by crashes or recoveries, and
so on. Many writers have studied the effects of trading institutions, trader behavior, and
feedback signals on such complex dynamic behavior, but the general problem remains
poorly understood. A classic dialogue about this issue can be seen, for example, in the
views of Friedman (1953) who argues that rational pro?t-seeking trading will always tend
to stabilize a free market, and a long succession of others (see, for example, Baumol, 1957
? Corresponding author. Tel.: +81-46-215-4965; fax: +81-46-273-7428.
E-mail address: e28193@jp.ibm.com (H. Mizuta).
0167-2681/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0167-2681(03)00019-2

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and de Long et al., 1990) who present models and accompanying arguments supporting
the idea that speculating traders who seek to maximize their pro?t can in some natural
circumstances destabilize a market.
In this paper, we study an agent-based simulation and focus on one particular question:
How is dynamic behavior affected when the price signal supplied to the agents is changed?
Brie?y stated, our main result is that a signal that is apparently only slightly richer in
information than the ticker price can dramatically stabilize our market—even when traders
operate with no planning or foresight whatsoever.
In the next subsection we will brie?y summarize the methods of attack on general ques-
tions of market stability and review previous work using what are called agent-based (or
microscopic) simulations. We will then describe the construction and general characteristics
of our own model.
1.2. Review of related work
The study of price movements in asset markets is remarkably complex: it combines
the problems of modeling human behavior with those of predicting the dynamic behavior
of very large, very nonlinear systems. Current approaches to the problem can be roughly
classi?ed as follows:
(a) Theoretical (analysis of mathematical models, usually using difference and differential
equations, and usually using aggregate variables).
(b) Empirical (econometric studies using real data).
(c) Experimental (laboratory studies using human subjects).
(d) Computational (simulations modeling the actions of individual agents—the approach
of the present paper).
Each has its advantages and disadvantages, and in some sense they are complementary,
contributing different and overlapping pieces to the puzzle. We next brie?y summarize
previous work in these areas with the goal of putting our own work in context.
Theory, the ?rst approach, is the oldest and most traditional in economics. It has the
important advantages of generality, and as all theory, it can guide intuition as well as provide
special tools for prediction and institutional design. The limitations of theory are equally
clear. It is all too easy to formulate reasonable equations that are beyond the reach of current
solution techniques. This is especially the case when studying markets with heterogeneous
agents and highly nonlinear trading rules. It is often necessary to simplify and aggregate
behavior to get results. The work of Caginalp and Balenovich (1994, 1996), which uses a
set of coupled nonlinear differential equations, is representative of this approach applied to
the study of market dynamics.
The second approach, empirical studies of asset prices, uses both conventional statistical
approaches and nonlinear dynamic models. The work centers on testing for the existence
of predictable structures in all kinds in time series. For a good review, especially of the
work on chaotic models, see Brock et al. (1991). Speci?cally, a number of studies in econo-
physics (for example, Mantegna and Stanley, 2000) have used concepts from statistical
physics and critical phenomena to study self-similarity and fat-tail distributions in empirical
data.

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237
The third approach, experimental economics, has the advantage of addressing more di-
rectly questions of human behavior. However, it is expensive, time-consuming, and it is
dif?cult to ensure that people behave the same way under laboratory conditions as they do
in real markets. Perhaps the most in?uential work is that of Smith, Plott, and their coworkers
(Forsythe et al., 1982; Smith et al., 1988; Smith, 1989; Porter and Smith, 1994; Caginalp
et al., 1998), which centers on the reproducibility of price bubbles. Along the same lines,
the collection of papers edited by Stiglitz (1990) on price bubbles is revealing in its diversity
of perspectives on just how a price bubble might be de?ned and whether in fact one can
exist at all.
Large-scale agent-based simulation, the fourth approach and the one used in this paper,
has become possible only relatively recently with the advent of fast, cheap, and readily avail-
able computers. It has been championed by physicists using the paradigm of computational
statistical physics. For example, de Oliveira et al. (1999) review several papers over the past
few years that exemplify the methodology, especially the work of Levy et al. (1994). The
reader is also referred to the recent paper of LeBaron et al. (1999), which also contains many
references to other work in this emerging ?eld. The de?ning characteristic of the method-
ology is that the actions of individuals are simulated, explaining the term microscopic. This
opens the door to the study of the interaction of large numbers of heterogeneous, interacting
agents.
An important theme that runs through much of the work in market dynamics is the
interaction between two kinds of traders: those who trade on “fundamentals” and those
who trade on “technical” information. The former are often called value traders, and the
latter noise traders, which include trend chasers (also called chartists). This interaction
accounts for the appearance of price bubbles in the simulations of Levy et al. (1994),
Youssefmir et al. (1996), and Steiglitz and his coworkers (Steiglitz et al., 1996; Steiglitz
and O’Callighan, 1997; Steiglitz and Shapiro, 1998), for example, as well as the aggregate
models of Caginalp and Balenovich (1994, 1996).
We mention important applications of agent-based simulations that are not directly eco-
nomic in nature: they can be translated literally into algorithms for distributed control of
resources (see, for example, the book edited by Clearwater, 1996). In these cases the agents
may well be distributed software agents instead of humans. Examples include computing
cycles (Waldspurger et al., 1992), network bandwidth, computer memory, electric power
(Ygge, 1998), or even thermal energy in a building. These applications need not necessarily
model realistic markets, but stability is obviously a key issue. More recently, Kephart et al.
(1998) anticipate the emergence of an open, free-market information economy of automated
agents buying and selling a rich variety of information goods and services on the Internet.
To characterize and understand the dynamic behavior of such information economies, they
very naturally employ agent-based simulation, and also use game theoretic analysis to in-
vestigate strategies and competition of software agents. As before, these markets do not
necessarily behave the way human markets do, but an understanding of stability is crucial.
1.3. Description of our model
The simulation model we use in this paper is a direct descendant of those described in
Steiglitz et al. (1996), and we outline its features in this section. The philosophy is to build

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the simplest possible system that can reasonably be thought of as a complete economy: in
some sense a minimal economy. Trade requires at least two commodities, so we use the
minimum of two, which we call food and gold. Gold plays the role of numeraire, and the
price of food is therefore measured in units of gold.
In general situation there are three types of agents: regular agents, value traders, and trend
traders. Regular agents can produce food or gold and consume food; value traders and trend
traders are solely speculators and play the roles of value and noise traders mentioned above.
The regular agents are completely myopic; that is, they exercise no foresight or planning.
One trading period of the market simulation is executed as follows. The central market
sends to each agent a Request For Bid (RFB) containing price signals. Consider ?rst the case
when the price signal is simply the previous closing price. Based on this signal, the regular
agents decide on their levels of production for that time step, the value traders update their
estimate of fundamental value, and the trend traders update their estimates of price trend.
The agents then send bids to sell or buy according to their food inventory (regular agent),
the difference between the market price and estimated fundamental price (value trader), or
the direction of the trend (trend trader). Finally, the market treats the submitted bids as a
sealed-bid double auction and determines a single price that maximizes the total amount of
food to be exchanged. This institution is sometimes called a clearing house or call market
as opposed to an open-outcry market (Friedman and Rust, 1993). The market-clearing price
(ticker price) becomes the next signal in the RFB. Note that in Steiglitz and O’Callighan
(1997) and Steiglitz and Shapiro (1998) the auctioneer determines the price to maximize
the total amount of gold to be exchanged. However, in practice this difference has little
effect on the overall qualitative results. Fig. 1 shows the derivation of the supply–demand
curves and market-clearing price in such an auction.
Consider next the regular agents. They follow a simple dichotomous algorithm: in each
trading period they can produce either food or gold. They make this production decision to
maximize pro?t, but in a shortsighted way, based only on the current price. Heterogeneity
Fig. 1. Generation of the supply and demand curves and market-clearing price in the double auction.

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239
is introduced by endowing agents with different “skills”—the amount of food and gold they
can produce per period. In a similarly shortsighted way they determine their bids to maintain
a ?xed food inventory, based only on their current inventory. The regular agents therefore
have no memory or foresight. Their strategy is so simple and myopic that it often throws
the market into confusion, in a way reminiscent of the cobweb model (Carlson, 1967).
We note that our model has a natural equilibrium price, or fundamental value, determined
by the equilibrium condition that total food produced is equal to the total food consumed.
This is one way that our model is distinguished from that of Levy et al. (1994), which gives
agents a choice between investments with certain and uncertain returns.
The remainder of the paper is organized as follows: in Section 2 we describe the results
of simulations using the original model, with market-clearing price as the signal, illus-
trating the stabilizing effect of value traders and the destabilizing effect of trend traders.
In Section 3 we describe the effects of using other price signals, speci?cally stabilization
without traders using unweighted and inversely weighted bid averages. Then, after some
concluding remarks, we present in Appendix A simpli?ed model and its analysis, con?rming
the results of the simulations.
2. Simulations
Markets with only such simple regular agents exhibit large price oscillations (see Fig. 2).
In these markets there is low trading volume, and most of the time there is a large overall
Fig. 2. Price vs. trading period with regular agents only and using closing price as a signal.

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Fig. 3. Average food inventory vs. logarithm of price in the same simulation as the previous ?gure, illustrating the
oscillation.
surplus or shortage of food. This oscillation can be visualized effectively by plotting a
two-dimensional graph of average food inventory versus log-price. The result is a diamond-
shaped cycle whose center is the ideal (equilibrium) price and ideal (desired) reserve (see
Fig. 3). This cycle starts close to the center and rotates counterclockwise with gradually
increasing radius. We cannot expect ef?cient resource allocation in such markets.
Fig. 4 shows a typical cycle of the oscillation, sketched diagrammatically in the food
inventory–price plane. We divide the cycle into four regions. In region I, the low price
prevents agents from producing food and the resulting de?ciency of food causes the price
to rise. In region II, when the price gets high enough, agents begin to produce food, but the
price keeps rising since there still is not enough food to satisfy demand. In region III, agents
now have enough food and the price begins to fall. However, they continue to produce food
because the price remains high for a time. In region IV, agents stop producing food because
the price ?nally becomes low. But the price continues to fall because of food surplus. It is
therefore the delay between the price movement and the size of the food inventory that brings
the system into oscillation, as in the cobweb model. However, this intuitive explanation only
goes so far and does not enable us to predict, for example, the radius of the cycle or in fact
whether a given system will be stable or unstable. One way to stabilize this market is to
introduce value traders who estimate the fundamental price (Steiglitz et al., 1996), thus
bringing a kind of foresight to market operations (see Fig. 5). As discussed above, the
introduction of trend traders can produce price bubbles, as illustrated in Fig. 6.

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241
Fig. 4. Diagrammatic representation of price oscillations in an unstable market in the plane of food inventory vs.
price.
Fig. 5. Price vs. trading period with value traders, showing how speculators can stabilize the market. Value traders
are introduced after 100 trading periods.

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Fig. 6. Price bubble caused by the introduction of trend traders. The fundamental value is exogenously driven up
and down to produce a trend. Value traders are introduced at period 100, after which the trading price remains
close to the fundamental value until bubbles appear near trading periods 530 and 610.
Until now we have described simulations with previous models, which made available to
the agents only the auction market-clearing price (ticker price) as a signal. This evidently
does not communicate enough information to stabilize the market without some memory
and foresight, which is invested in the value traders, who use an exponentially smoothed
estimate of fundamental value. We next consider the possibility of using signals other than
the market-clearing price to achieve stability.
3. Using other price signals
Consider again the market with only regular agents. After consuming one unit of food,
each agent sends a bid pi and a quantity ai to be traded, both depending on the price signal
as well as the difference between the agent’s food inventory and his desired reserve. This
bidding process generates at any given trading period an order book, comprising the agents’
bid prices pi and amounts ai. This order book contains considerably more information about
market conditions than simply the most recent closing price. This suggests that we can derive
signals from the order book that can be more effective in stabilizing prices than the closing
price. In practice it is this information that gives commodity traders in the pit an advantage
over remote traders.

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243
Fig. 7. Price vs. period with no traders, but using average bid, P0, as the signal.
Consider ?rst the simplest possibility: de?ne the new signal P0 to be the unweighted
average of all the bid prices:
P0 = 1
p
n
i
(1)
i
Fig. 7 shows that the price is stabilized quite well, although the time to convergence is
longer than with value traders.
Having observed the effectiveness of the mean bid as a signal, it is natural to try to
improve it further, and a natural choice is the average of the bids weighted by the amounts
P1:
P1 = 1
a
a
ipi
(2)
i i
Fig. 8 shows the result, which is perhaps surprising: weighting the bids by the amounts has
the effect of destabilizing, rather than further stabilizing the market.
Finally, this suggests moving in the opposite direction: weighting the prices by some
function that varies inversely with the corresponding amount. We therefore de?ne P2 to be
P
1
2 =
1
pi
(3)
1/(c + ai)
c + a
i
i
where c is a scaling parameter that determines the extent of inverse weighting. The value
c = 1 was used in the simulations in this paper. Fig. 9 shows that the market with signal P2
converges faster and better than with P0.

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Fig. 8. Price vs. period with no traders, using the weighted average bid, P1, as the signal.
Fig. 9. Price vs. period with no traders, using the inversely weighted average bid price, P2, as the signal.

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Document Outline

• Effects of price signal choices on market stability
  • Introduction
    • The problem of market stability
    • Review of related work
    • Description of our model
  • Simulations
  • Using other price signals
  • Concluding remarks
  • Appendix A
    • The simplified model
    • Simplified model with signal P0
    • Simplified model with other signals
  • References

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