Evolution with Individual and Social Learning in an Agent-Based Stock Market
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Evolution with Individual and Social Learning in an Agent-Based Stock Market Ryuichi YAMAMOTO Brandeis University 0. ***Review*** * What are about an Agent-based Stock Market? Deals with stock market A set of interacting heterogeneous agents Learning/Adaptation/Evolution Market Market

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Evolution with Individual and Social Learning in an Agent-Based Stock Market Ryuichi YAMAMOTOBrandeis University


0 review what are about an agent based stock market l.jpg
0. ***Review*** Agent-Based Stock Market * What are about an Agent-based Stock Market?

  • Deals with stock market

  • A set of interacting heterogeneous agents

  • Learning/Adaptation/Evolution


0 review what are individual learning and social learning l.jpg

Market Agent-Based Stock Market

Market

0.***Review*** What are Individual Learning and Social Learning?

Figure 2: Social Learning:

Figure 1: Individual Learning

  • The previous literature doesn’t say anything why agents choose a particular level of learning…..

Privately distributed

Imitative behavior


1 what i do l.jpg
1. ***What I do***: Agent-Based Stock Market

Evolution with individual “and” social learning


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  • ….LeBaron (2000) and Arthur et al. (1996)

  • The economy with more intelligent agents cannot reach the REE. Intelligent agents are not rational.

    2) Which learning dominates the market?

  • Only wealthy agents often pick an idea from individual learning while other agents imitate others.


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    Outline expectation equilibrium (REE)?

    0) Preview

    • What I do

    • Market structure

    • Computer Simulations

    • Conclusion


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    2. ***Market Structure*** expectation equilibrium (REE)? (LeBaron et al. (1999))

    • 2 tradable assets: a stock and a bond.

    • The risk-free bond: =10%.

    • The stock pays a dividend:

    • # of shares is 30 = # of agents in the market.


    How do events in this artificial market proceed 1 information set l.jpg
    *** How do events in this artificial market proceed? *** expectation equilibrium (REE)?1. Information set:

    • At time t, agents observe the past price and dividend, and calculate technical indicators.

      where k=1 and 2.

    • =0.8 for and =0.99 for .

    • Form an information set, ‘ ’.


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    2. Prediction expectation equilibrium (REE)?:

    • LeBaron (2002):


    Slide11 l.jpg


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    3. Strategy making ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and , :

    4. Price determination:


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    5. Volume determination and updating wealth: ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and ,

    • After revealing the price, trading volume is recorded.

    • Wealth, w, for individual i is evolved according to:


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    6. Updating Forecast Strategies ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and , :

    • Step 1-5 are repeated for 25 periods.

    • Figure 4: Timing of the market:

    • The fitness criterion :

    25 50 ……………………….. 500


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    Evolution with individual ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and , “and” social learning


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    3. ***Experiments*** ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and ,

    • Simulations are repeated for 10 times.

    • The series of stock price, dividend, and volumes are recorded for the last 5,000 periods.

    • Following LeBaron et al. (1999), the estimated residual series ‘ ‘are analyzed for the REE.


    3 1 are intelligent agents rational l.jpg
    3.1 ***Are intelligent agents rational?*** ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and ,

    • Given a time horizon, can an economy with intelligent agents reach a rational-expectation equilibrium?

    Table 1: Summary Statistics


    Results l.jpg
    Results ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and ,

    • The economy with more intelligent agents cannot reach the REE. -> Intelligent agents are not rational.

    • Why? -> b/c the forecast strategies reflect information in past 25 periods.

    • Consistent with actual markets?: Investors in 40 years ago.


    3 2 which level of learning dominates the market l.jpg
    3.2 ***Which Level of Learning Dominates the Market?*** ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and ,

    • Who chooses which level of learning and what proportion of the agents often uses individual or social learning?

    • (Which learning is more likely to produce better ideas?)


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    Data: ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and ,

    • Figure 4: Timing of the market:

      25 50 ……………………….. 500

    • The matrix on the choices eventually becomes 30x200.

    • For the matrix on wealth, the wealth of each agent over a generation is summed up. 30x200.

    • How are the wealth levels related to the choices?


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    Model: ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and ,

    (17) P(Choice=1|wealth) =

    • Standardize a variable, WEALTH.

    • The parameters, and, are estimated by the maximum likelihood method.


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    Analyses: ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and ,

    • The estimated probabilities (30x200) and the wealth variable are compared for all 30 agents and for all 200 generations. => What do we expect?

    • First, consider agents with “more than average” wealth and with “less than average” wealth. The estimated probabilities are categorized into “more than 0.5” and “less than 0.5”.

    • Second, examine the behavior of agents with “really high wealth”.


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    • **(Case 1)**: ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and , Agents with “more than average wealth” are more likely to choose ideas from individual learning while agents with “less than average wealth” are more likely to choose ideas from social learning.

    • **(Case 2)**: Agents with “more than average wealth” are more likely to choose ideas from social learning while agents with “less than average wealth” are more likely to choose ideas from social learning also.


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    • **(Case 1)**: ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and , Agents with “Highest wealth” are more likely to choose ideas from individual learning while other agents are more likely to choose ideas from social learning.

    • **(Case 2)**: Agents with “Highest wealth” are more likely to choose ideas from social learning while other agents are more likely to choose ideas from social learning also.


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    Results ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and ,

    • Agents use their private ideas more often than the others do only when they have really high wealth.

    • Social learning dominates the market.

    • Most agents would be better off in an ex ante welfare sense by constraining the use of their own ideas. (herd behavior)

    • Consistent with actual markets?


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    Conclusion ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and ,

    • Evolution with individual and social learning

    • The economy with more intelligent agents cannot reach the REE. -> Intelligent agents are not rational.

    • Social learning dominates the market.


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