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Introduction to Three ApproachesIntroduction to Three ApproachesIntroduction to Three Approaches Introduction to Three Approaches to to EconophysicsEconophysics

Jiping Huang (黄吉平)

Department of Physics, Fudan University, Shanghai , China

Welcome to Welcome to FudanFudan

—Soft matter and interdisciplinary research groupy g

Fudan’s Main Entrance Guanghua Bld.

EconophysicsEconophysics in the Eye of Economists in the Eye of Economists

• Econophysics is having some impact on the more applied field of quantitative finance.

• Various econophysicists have introduced models for price fluctuations in financial markets.

• Papers on econophysics have been published primarily in journals devoted to physics and statistical mechanics, rather than in leading economics journals. –Submission fee is also a factor!?

• Many mainstream economists have been unimpressed by them. (Armed with i k l d ! C b t h t i t b t!)economics knowledge! Care about what economists care about!)

LooooooooooooongLooooooooooooong way to go. gg y g

AcknowledgementsAcknowledgements

W Wang (09’PHD) Y Wang (09’PHD)JR Wei (08’PHD) L Zhao (10’PHD) Y Liang (10’PHD)

XX Zhao (08’MSC) XW Meng (09’MSC) YY Qiu (09’MSC) KY Song (09’MSC)T Qiu (10’PHD)

OutlineOutline

Background1

Approach I: Statistical analysis2

Approach II: Modeling3

Approach III: Controlled experiments4

Conclusions5

Background: Background: Physics Physics vsvs EconomicsEconomics

PHYSICS: Rockets fly to the moon, energy is extracted from minute changes of atomic mass without major havoc, global positioning satellites help millions of people to find their way home……

ECONOMICS: What is the flagship achievement of economics,

VS

g p ,apart from its recurrent inability to predict and avert crises, including the current worldwide financial crisis?

Compared to physics, it seems fair to say that the quantitative success of the economic sciences is disappointingsuccess of the economic sciences is disappointing.

EconophysicsEconophysics

d b l• Coined by H. E. Stanley

(1995，NAS member)(1995，NAS member)

•• EconophysicsEconophysics:: “See

economic problems from

h i l i f i ”physical point of view”

• VERY far from being well‐VERY far from being well

developedwith H. E. Stanley

A Paradigm in Standard EconomicsA Paradigm in Standard Economics

A.More qualitative than quantitative! (Sure, not all! E.g., finance, quantitative economics …)– As a social science!

B.Take an example: The “Invisible Hand”

k h b ll “ ”Free markets appearing chaotic and unrestrained, but essentially “ordered” Adam Smith assume the existence of an “invisible hand” Used the “invisible hand” to successfully explain many many phenomenad th t dand thus suggested:

• Government does not need to do anything The great depression 1929‐1932 causes corrections to the “invisible hand”:Specific conditions must exist for the “invisible hand” to play a roleSpecific conditions must exist for the invisible hand to play a role,And thus economists suggested an inverse proposal to ensure the “conditions”:• Government needs to macroscopically manipulate The latest financial crisis offers again challenges to the existing macroscopicThe latest financial crisis offers again challenges to the existing macroscopic manipulation?? … …

The Paradigm in PhysicsThe Paradigm in Physics

Theory:Modeling with analytic theory/computer l h l l hsimulations Phenomenological + Basic theory

+Experiment: Experimental observation Rules

Confirm theory

A li i

Confirm theory

Applications

The Paradigm in The Paradigm in EconophysicsEconophysics

Experiment: Experimental observation based on financial/economic data + controlled xperiments/ p Rules

+Theory: Modeling with analytic theory/computer simulations Phenomenological + Basic theory

+

simulations Phenomenological + Basic theory

Confirm theory

Applications——(Possible) Policy Predictions

EconophysicsEconophysics is a subis a sub--branch of physicsbranch of physics

• Physics: Statistical mechanics (containing thermal dynamics), classical mechanics,

quantum mechanics and electrodynamicsquantum mechanics, and electrodynamics

• Econophysics: Statistical mechanics, classical mechanics, quantum mechanics (?), and

electrodynamics (?)electrodynamics (?)

• Not as close to them as (traditional) physics, which, however, maybe drives us to

conduct more research due to the analogyconduct more research due to the analogy

• BTW, econophysics belongs to complex system science. Economic markets can be seen

ki d f l fl id t i l t di d i ft tt h ias a kind of complex fluids, extensively studied in soft matter physics.

Three approaches to Three approaches to econophysicseconophysics

•• Statistical analysisStatistical analysisApproach IApproach I

•• Modeling Modeling (computer simulations + analytical theory)(computer simulations + analytical theory)Approach IIApproach II

•• Controlled experiments Controlled experiments ( ith t( ith t b d d li )b d d li )Approach IIIApproach III (with agent(with agent--based modeling)based modeling)Approach IIIApproach III

Approach I: Approach I: Statistical analysisStatistical analysis

•• based on existing financial/based on existing financial/ecomonicecomonic datadatagg•• achieves empirical lawsachieves empirical laws

Fat tailExample： Fat tail[Nature 376, 46 (1995)]

Example：-Non-Gaussian distributions in financial market fluctuations, with scaling law (mechanism?)

The non‐gaussian distribution was soon demonstrated to be universal for stock prices, and has attracted

Scaled plot of the probability distributions P z of the S&P 500 index variations z t .

g p ,the great interest of economists because of the breakdown of the gaussian distribution previously commonly recognized by economists .

Approach II: ModelingApproach II: Modeling

•• AgentAgent based modelingbased modeling (As do economists econophysicists view the•• AgentAgent--based modeling based modeling (As do economists, econophysicists view the economy as a collection of interacting units/agents)

•• Non agentNon agent--based modeling (E.g., price dynamic modeling)based modeling (E.g., price dynamic modeling)

Examples for ModelingExamples for Modeling (computer simulations)(computer simulations)

Modeling a Complex Adaptive System (CAS): El Farol Bar problem

outcome

compete evaluate

t t tagent strategy

select

W. B. Arthur, American Economic Review (Papers and Proceedings) 84,406 (1994)


Minority Game (MG) – an agent-based model

0 1decisionInformation

One model strategy (m=2)

00 110 0

decisionInformation in memoryM1=M2

Population

N (odd)

01 111 000 1m2

(Different but same preferences)

01 1…10010101 history

Has been extensively Look at last m (here m= 2) bits of history

The total decision gives the winning side:the minority one

Has been extensively applied to complex adaptive systems including stock markets!

D. Challet & Y.-C. Zhang, Physica A 246, 407 (1997)


An extension of Minority game, MDRAG for biased resources M1 ≠ M2

outcome

H t

compete evaluate

Heterogeneous Preferences

agent strategyagent strategy

select

Market‐Directed Resource Allocation Game (MDRAG)

W. Wang, Y. Chen & J. P. Huang, PNAS 106, 8423 (2009)


situation choice situation choice

A. MG B. MDRAG

situation choice

1 0

2 1

situation choice

1 1

2 1

… …

P-1 0

P 1

… …

P-1 1

P 1

For each situation, choice will be given as:50% for “0”

Number of 1 Probability

0 1/(P+1)

1 1/(P 1)50% for 050% for “1”

1 1/(P+1)

… …

P-1 1/(P+1)

P 1/(P+1)

So the choice in Table A is possible for MG;So, the choice in Table A is possible for MG;The choice in Table B is practically impossible for MG

Examples for ModelingExamples for Modeling (analytical theory)(analytical theory)

The Black-Scholes equation for options pricing

• 1827 Brownian motion — seemingly random movement of pollen particles suspended in water

• 1900 Louis Bachelier A stochastic analysis of the stock and option markets

• 1905 Albert Einstein’s formulatS

• 1959 M.M. Osborne: Independent stochastic parameter should be price log‐ return ln p t dt ‐ln p t

tDx

• 1973 Fischer Black and Myron Scholes: The Black‐Scholes equation for options pricing Assumed that the price follows a geometric Brownian motion with constant drift and volatility . Outcome of the marriage between finance theory in economics/finance and diff sion theor in ph sics !diffusion theory in physics !

• 1997 Robert C. Merton and Myron Scholes received the Nobel Prize

Approach III: Controlled experimentsApproach III: Controlled experiments

• Inspiring from Behavioral Economic Experiments

• Controlled!! It is illegal to control real markets

• More looks like what “experiment” means in the field of traditional physics

An example for Controlled experimentsAn example for Controlled experiments

Resource allocation based on MDRAG

• Biased distribution

Game Rules:

• Share the resource

• Relative minority win

• No communication

• Exchange to RMB (¥)

M1/N1 > M2/N2 or M1/M2>N1/N2 -> “1” winM /N < M /N or M /M <N /N -> “2” winM1/N1 < M2/N2 or M1/M2<N1/N2 -> 2 win



GAME I: Experimental results

• M1, M2, M3, N1, N2 and N3 are known.

Times Group Rounds M1 M2 M3 <N1> <N2> <N3>

1 A(N=12) 10 3 2 1 5.3 4.6 2.1

2 A(N=12) 10 3 2 1 5 5 3 8 2 72 A(N=12) 10 3 2 1 5.5 3.8 2.7

3 B(N=12) 10 3 2 1 5.5 4 2.5

4 C(N=24) 20 3 2 1 12.2 7.4 4.4

5 D(N=10) 10 5 3 ‐ 6.1 3.9 ‐

6 D(N=10) 10 3 1 ‐ 7.4 2.6 ‐

The “invisible hand” seems to appear!



GAME II : Experimental results

Ti G R d M M <N > <N >

• M1, M2, N1, N2 are unknown.

Times Group Rounds M1 M2 <N1> <N2>1 D(N=10) 10 2 1 6.2 3.82 E(N=10) 10 1 3 3.3 6.7( 0) 0 3 3 3 63 F(N=11) 1~10 3 1 7.2 3.83 F(N=11) 11~20 3 1 8.3 2.74 C(N=24) 1~15 7 1 17.8 6.24 C(N=24) 16~30 7 1 21.1 2.9

Relaxation time

“ ”The “invisible hand” seems to appear!



GAME III : Experimental results

Times Group Rounds M M <N > <N >

• M1/M2 was changed without announcement.

Times Group Rounds M1 M2 <N1> <N2>

1 G(N=10) 1~5 3 1 5.4 4.6

1 G(N=10) 5~10 3 1 8.2 1.8

1 G(N=10) 11~15 3 1 7 3

1 G(N=10) 15~20 3 1 7 3

1 G(N=10) 21~25 1 3 7 8 2 21 G(N=10) 21 25 1 3 7.8 2.2

1 G(N=10) 26~30 1 3 4.2 5.8

1 G(N=10) 31~35 1 3 2.8 7.2

1 G(N=10) 36~40 1 3 2.6 7.4

1 G(N=10) 41~45 1 3 2.4 7.6

Th “i i ibl h d” i h d l d i !The “invisible hand” seems to appear in the modeled economic system!



2 rooms2 rooms2 rooms2 rooms

Results of MDRAG is in goodResults of MDRAG is in good

agreement with experiments:

<N >/<N >=M /M<N1>/<N2>=M1/M2

Larger S will improve the

f i b th MDRAGperformances in both MDRAG

and MG

Computer simulation of GAME II (N=24);

According to Approach III, we have presented a direct experimental realization for Computer simulation of GAME II (N 24);

Strategy payoff = 1(win) or 0(lose); P=16experimental realization for MG/MDRAG

ConclusionsConclusions

Have briefly reviewed three existing approaches to econophysicsApproach I: Statistical analysisApproach I: Statistical analysisApproach II: Modeling (computer simulations + analytical theory)Approach III: Controlled experiments (with agent-based modeling)

Have presented some relevant examples

A i t diti l h i A h III i ht b t th d fAs in traditional physics, Approach III might serve as a robust method for econophysics. And it would be better for us to pay more attention.

According to Approach III, we have presented a direct experimental realization for MG/MDRAG

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Introduction to Three Approaches - ScienceNet.cnblog.sciencenet.cn/upload/blog/file/2010/8/20108261916125753.pdf · Introduction to Three Approaches ... economy as a collection of