How to Deal with Emergent
Behavior in Finance Markets?
Akira Namatame
National　Defense Academy，Japan
www. nda.ac.jp/~nama
0 - APWIES ’06 (Seoul)
Summary of the talk
(1) Emergence: Natural Laws in Manmade Systems
ΠEmergence by nature vs. Emergence by design
ΠHow can we recognize emergence?
(2) Efficient Market Hypothesis (EMH) vs.Interacting
Agent Hypothesis (IAH)
(3) Challenges in controlling emergence in finance
markets
1 - APWIES ’06 (Seoul)
What is emergence?
Œ
Emergence by nature (empirical view)
: Systems self-organize into a complex state,
poised between predictable cyclic behavior
and unpredictable chaos
Œ
Emergence by design (operational view)
: System-wide behavior remerges from
interactions among individual elements
2 - APWIES ’06 (Seoul)
Examples of Emergence by Nature
(K. Mills, 2004)
3 - APWIES ’06 (Seoul)
Examples of Emergence by Design
(K. Mills, 2004)
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How can we recognize emergence?
Research Agenda
Œ
Do markets inherently exhibit emergent behaviors?
–If so, are the behaviors desirable, undesirable, or mixed?
– If so, can we explain, predict, and exploit the behaviors?
•　Can we devise effective decentralized mechanisms to
elicit desired emergent properties?
6 - APWIES ’06 (Seoul)
Two Competing Hypotheses in Financial Markets
Efficient Market Hypothesis (EMH) vs.
Interacting Agent Hypothesis (IAH).
Traditional Efficient Market Hypothesis( Samuelson (1955), Fama (1987))
⇒　Traders are rational
⇒　Price movement is random walk!
⇒　No traders accumulate their wealth in the long-run
and they do only by chance （no winning strategy）
7 - APWIES ’06 (Seoul)
A Microscopic Behavior Model
•Probability to buy
Buy
Sell
p１ = 1 / (1+exp(-(V1- V2)))
•Probability to sell
p2 = 1 / (1+exp(-(V2- V1)))
Utility of buy　V1
Utility of sell　V2
p１ Probability to buy
1.2
Trader’s choice
0
-6
-4
-2
0
2
V1 – V2
4
6
Probability to buy:　p1
8 - APWIES ’06 (Seoul)
Aggregated behavior
(McFadden, 1981） •Probability to buy
p1 = Pr(U1 > U 2 ) = Pr(V1 + ε 1 > V2 + ε 2
ε1,ε2：Gumbel function F(x)=exp{-exp(-κx)}
p1 = 1 /[1 + exp{−κ (V1 − V2 )}
1 .2
0
-6
-4
-2
0
2
V1-V2|
4
6
If parameter κ is small : p=0.5
aggregated behavior of buying is a kind of random
walk!
9 - APWIES ’06 (Seoul)
Financial Puzzles (1)
More agents buy
Price
Priceup
up
More agents sell
Price
Price
down
down
What
Whatisisititthe
thedifference
differencebetween
betweensuccessors
successorsand
andfailures?
failures?
10 - APWIES ’06 (Seoul)
Financial Puzzles (2)
Investors are not always rational.
They behave under illogical, limited rationality, and
many different models for investors have been proposed.
• Chartists: look at chart
• Fundamentalists: consider a right price
• Noise traders:behave randomly
•Imitators
Why different trading types coexist(survive)
?
11 - APWIES ’06 (Seoul)
Stylized Facts of Stock Market
Financial data exhibit a number of empirical regularities of
both conditional and unconditional properties of the time
series:
ƒ
ƒ
ƒ
ƒ
: Absence of correlation in returns, (near?) martingale
behavior.
: Non-Gaussian character of the unconditional distribution
: Power law decay of the tail with an exponent α≈3.
: Volatility clustering, and long-range dependence in
volatility.
These empirical findings are very robust (universal) for all
high- frequency data across markets and assets.
(T. Lux, 2006)
Return: pt-pt-1
Return: pt-pt-1
Interacting Agent Hypothesis (IAH)
Agent-based Financial Markets
Œ
Œ
Many heterogeneous traders (agents)
Endogenous heterogeneity
• Different trading behavior
• Different learning models,…
14 - APWIES ’06 (Seoul)
Ising model
・The probability to buy
p１ = 1 / (1+exp(-2β hi(t))
hi(t)=ΣJijSj(t)-αSi(t)|M(t)|
Neighbors’ behavior
Market behavior
Jij:Influence from neigh bors　α,β:constants
S:Buy+1Sell-1　The average
1.2
p１ = 1 / (1+exp(-2β hi(t))
ΣJijSj(t)
M(t)
Conforms to neighbors
0
Adapt to the aggregate
-6
-4
-2
0
2
4
6
hi(t)=ΣJijSj(t)-αSi(t)|M(t)|
0.08
0.06
0.04
0.02
04
/9
/3
0
04
/7
/3
1
04
/5
/3
1
04
/3
/3
1
04
/1
/3
1
03
/9
/3
0
03
/1
1/
30
-0.04
03
/7
/3
1
-0.02
03
/5
/3
1
03
/3
/3
1
0
03
/1
/3
1
Strategy decision
-0.06
-0.08
-0.1
-0.12
Price movement
15 - APWIES ’06 (Seoul)
Agent-based models of financial markets
ƒDe Long et al. (1990): Irrational Noise Traders
ƒ Baumol (1957), Frankel and Froot (1986), De Grauwe et al.
(1993): Fundamentalists and Chartists
ƒ Kirman (1993): Herding among traders
ƒ Lux and Marchesi (1999): fundamentalists and noise
traders/chartists switch between groups in some sort
of social interaction.
A Basic Agent Model
Œ
Œ
Œ
Agents face binary choices: “Buy” or “Sell”.
Agents have stock and cash.
Each agent trades 1 unit in one trade.
Stock Price Model
„ P(t+1) = P(t) + χ(N1(t)-N2(t))
P(t):Stock price at time t.
N1(t): The number of agents to ”Buy” at time t
N2(t):The number of agents to ”Sell”at time t.
χ:price elasticity
17 - APWIES ’06 (Seoul)
Two Types of Social Interaction
Œ
Œ
Coordination problems
Peoples are better off if they take the same action.
This type of social interaction is formulated as
“coordination games”.
Dispersion problems
Peoples are better off if they take
the distinct actions.
This type of social interaction is formulated
as “minority (dispersion) games”.
18 - APWIES ’06 (Seoul)
Finance market: The Minority Game
0 (buy)
majority
Choose 0,1
1 (sell)
N traders
minority
win
The price will up since there are more buys
19 - APWIES ’06 (Seoul)
El Farol bar Problem as Minority Game
[W. B Arthur(1994)]
A
B
…
20 - APWIES ’06 (Seoul)
Aggregated Behavior
Blue# of agents to go bar
Red：# of agents to stay
home
Number of Agents
capacity
Homogeneous agents with
the same expectation
Heterogeneous agents with
different expectations
21 - APWIES ’06 (Seoul)
Minority Game among Learning Agents (1)
<Limited intelligence>
ΠAgents use only the public information of which
choice win
ΠS and M are relatively small
Πstrategies do not change
<Heterogeneous agents by learning>
ΠBest-scored strategy changes by time
22 - APWIES ’06 (Seoul)
Minority Game among Learning Agents (2)
ŒAgents
use only the public information of which choice win
History
2
3
Strategy1
Strategy2
Strategy3
Strategy4
0
0
0
1
0
1
0
0
0
1
0
0
0　0
0
1
0
0
0
1　1
0
1
1
0
1
0
1
1
0
0
1
0
1　0
1
0
1
0
0
0　1
1
1
0
1
1
1　1
1
1
1
1
1
0　0
5
0
2
-1
Point
2
23
23 - APWIES ’06 (Seoul)
Performance of Aggregated Behaviour
Not too little memory, and not too much memory
efficiency
σ = < ( A − N / 2) 2 >
A:# of agents to go bar
σ
[Challet and Zhang (1997)]
m:length of memory
24 - APWIES ’06 (Seoul)
Individual Learning vs. Social Learning
The previous literature doesn’t say anything
why agents do not learn each other (co-evolution)
Market
Market
Privately distributed
Imitative behavior
25 - APWIES ’06 (Seoul)
Rational trader (Contrarian) vs. Imitator
Rational traders:
(1) If stock price is expected to go up, then they buy.
(2) If stock price is expected to go down, then they sell.
Imitator:trend follower, momentum trader)
(1) If the majority of rational traders “buy”, then imitators also “buy”.
(2) If the majority of rational traders “sell”, then imitators also “sell”.
26 - APWIES ’06 (Seoul)
Simulation Conditions
Œ
Œ
Œ
Population of traders: 2,500
The ratio of rational traders: 20-80%
Market condition:
Case 1 If ”Sell” is bigger than ”Buy”
agents with more stock can sell.
Case 2 If ”Buy” is bigger than ”Sell”
agents with more cash can sell.
27 - APWIES ’06 (Seoul)
Trading Rule of Rational Trader
Forecast of trader for the next proportion to ”buy”
Ri(t+1) = R(t) + ε
R(t) : The ratio of ”buy” at time t.
Trading Rule:
If Ri(t+1)< 0.5, then “Buy”
If Ri(t+1)> 0.5, then “Sell”
28 - APWIES ’06 (Seoul)
Trading Rule of Imitator
Rs(t): The ratio of strategic traders to ”buy” at t.
The forecast of the imitator j with respect to the ratio of
strategic traders to ”buy” at time t+1
Rj(t+1) = Rs(t) + ε
ε :Degree of bullish and timid. (-0.5 < ε < 0.5)
Trading Rule:
If Rj(t+1)>0.5 then “Buy”
If Rj(t+1)<0.5 then “Sell”
29 - APWIES ’06 (Seoul)
Simulation result
Case 1: Strategic trader:20%, Imitators:80%
The average wealth
Wealth distribution as the function of ε
1200000
800000
■Strategic trader
■Imitators
600000
400000
-0.6
200000
-600000
-0.4
TIME
-0.2
-100000
0
0.2
0.4
0.6
-600000
timid
-400000
900000
400000
1
48
95
142
189
236
283
330
377
424
471
518
565
612
659
706
753
800
847
894
941
988
0
-200000
■Imitators
W EALTH
AVER AGE W EALTH
1000000
1400000
■Strategic trader
-1100000
ε
bullish
-1600000
30 - APWIES ’06 (Seoul)
Simulation result
Case2: Strategic trader: 70%, Imitators:30%
Wealth distribution depending on ε
The average wealth
■Strategic trader
1000000
■Imitators
AVER AG E W EALTH
1200000
■Strategic trader
1400000
■Imitators
900000
W EALTH
800000
600000
400000
200000
-0.6
-200000
1
47
93
139
185
231
277
323
369
415
461
507
553
599
645
691
737
783
829
875
921
967
0
-400000
-600000
400000
-0.4
-0.2
-100000
0
0.2
0.4
0.6
-600000
timid
bullish
-1100000
-1600000
TIME
ε
31 - APWIES ’06 (Seoul)
Simulation result
Case3: Strategic trader: 80%,Imitators: 20%)
The average wealth
1200000
■Strategic trader
■Strategic trader
1400000
■Imitators
■Imitators
W EALTH
1000000
AVER AG E W EALTH
Wealth distribution depending on
800000
600000
-0.6
400000
200000
900000
400000
-0.4
-0.2
-100000
0
0.2
0.4
0.6
-600000
0
-1100000
1
47
93
139
185
231
277
323
369
415
461
507
553
599
645
691
737
783
829
875
921
967
-200000
ε
-400000
timid
bullish
-1600000
ε
-600000
TIME
32 - APWIES ’06 (Seoul)
Accumulation of wealth of successor:
strategic traders: 20%
Change of wealth
Bullish trader
(ε = 0)
Change of wealth (ε = 0.35)
1800000
1600000
1400000
1200000
1000000
800000
600000
400000
1800000
1600000
200000
0
1200000
1000000
800000
600000
400000
Normal traders:
stocks and cash are
in a balance.
1
49
97
145
193
241
289
337
385
433
481
529
577
625
673
721
769
817
865
913
961
1
49
97
145
193
241
289
337
385
433
481
529
577
625
673
721
769
817
865
913
961
200000
0
TIME
(ε = -0.35)
W EA LTH
w e a lt h
800000
600000
400000
Change of wealth
1800000
1600000
1400000
W EA LTH
1400000
1200000
1000000
Timid trader
TIME
Bullish traders:Asset is
held by many stocks.
The total assets are not
steady because of the
change of stock prices
200000
0
-200000
1
49
97
145
193
241
289
337
385
433
481
529
577
625
673
721
769
817
865
913
961
Normal trader
TIME
Timid trader sell
many stocks, and
the assets are held
by cash.
33 - APWIES ’06 (Seoul)
Changing the ratio of rational traders
Actual price movement
Rational trader20%, imitator：80%
Random change of rational traders
14000
12000
12000
10000
10000
8000
6000
8000
4000
6000
2000
4000
0
11
21
31
41
51
61
71
81
91
時間
2000
35
33
31
29
27
25
23
21
19
17
15
13
9
11
7
5
0
3
1
1
株
価
Increment of rational traders by 10%
14000
12000
10000
8000
6000
4000
2000
0
1
2
3
4
5
6
7
8
9
10
11 12
13 14
15 16
17 18 19
20 21
22 23
24 25
26 27
28 29
30 31
32 33
34 35
34 - APWIES ’06 (Seoul)
Controlling Emergent Behaviour
Which trading types will prevail in the market?
: The ratios of agent types determine, not the strategy.
Strategic traders
Imitators
By changing the ratio of trader types, we can fairly
control emergent behavior in a finance market.
35 - APWIES ’06 (Seoul)
Conclusion
Emergence: Two Basic Research Agenda
<The forward problem>
: Analysis，Explanation, Understanding
<The inverse problem>
Desired collectives
: Design agent rules through learning
: Change the combination of heterogeneous
agent types
Emergent
Emergent
Inverse problem behavior
behavior
Forward problem
36 - APWIES ’06 (Seoul)
Interacting agents with micro-motives
Final remark:
How should agents learn in the context of other learners?
preference
Collective
Agent
Learning
‰ Equilibrium agenda (Game theory):
How simple adaptive rules lead the agents to an equilibrium?
(It is not required any optimal requirement).
‰ AI agenda (Multi-agents learning):
What is the best learning algorithm?
‰ Collective learning agenda:
How should agents learn to realize a “desired collective”?
37 - APWIES ’06 (Seoul)
New book: World Scientific, 2006
38 - APWIES ’06 (Seoul)
Thank you!! and
Question time
39 - APWIES ’06 (Seoul)
Some traits common to emergent systems
•Autonomous action–individual elements act independently without
benefit of a master control element
•Local information–elements act based on (physically or logically) local
information without benefit of a global view
•Dynamic population–elements added and deleted naturally without
system survival depending on individual elements
•Collective interaction–system behavior arises from interactions among
many similar independent elements
•Adaptation–individual elements can adapt to changing goals,
information, or environmental conditions
•Evolution–individual elements possess the ability to evolve their
behavior over time
40 - APWIES ’06 (Seoul)
How does emergence arise?
Scale–requires critical mass in the number of system elements (order
emerges from many interactions over space and time)
•Simplicity–requires that each element behave rather simply (difficult to
construct elements to act on complete information)
•Locality–requires interaction among “neighbors” (limits speed of
information dissemination)
•Randomness–requires chance interactions among elements (increases
degree of information dissemination)
•Feedback –requires ability to sense environmental conditions (allows
some estimation of global state)
•Adaptation–requires that each element can vary its behavior(allows
system state to change with time)
Œ
41 - APWIES ’06 (Seoul)
Emergence by Design vs. Emergence by Nature
Œ
Œ
Œ
By Design–some researchers view emergence as a property
that is “designed” into systems–Inspires research into
techniques to generate desired emergent behaviors
By Nature–some researchers view emergence as an “innate”
property of natural systems–Inspires research to discover and
explain emergent behaviors
Possible implications for information systems–Some
researchers think we should investigate models (such as
artificial life, cellular automata, swarms, biomorphic
software, and intelligent agents) to generate emergent
behavior in information systems–Some researchers suspect
that large-scale information systems inherently exhibit
emergent properties
42 - APWIES ’06 (Seoul)