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

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

2. 0. ***Review**** What are about an Agent-based Stock Market? • Deals with stock market • A set of interacting heterogeneous agents • Learning/Adaptation/Evolution

3. 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

4. 1. ***What I do***: Evolution with individual “and” social learning

5. Would the economy with intelligent agents reach a rational expectation equilibrium (REE)? • ….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.

6. Outline 0) Preview • What I do • Market structure • Computer Simulations • Conclusion

7. 2. ***Market Structure*** (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.

8. *** How do events in this artificial market proceed? ***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, ‘ ’.

9. The information set, ‘ ’, includes: 1) 2) 3) 4) 5) * At time t, dividend, , is revealed and paid.

10. 2. Prediction: • LeBaron (2002):

11. Permitting to range ‘ ’ with the allowable bounds for ‘ ’ and ‘ ’ as in LeBaron (1999), that is, and , • Agents are heterogeneous in terms of their expectation.

12. 3. Strategy making: 4. Price determination:

13. 5. Volume determination and updating wealth: • After revealing the price, trading volume is recorded. • Wealth, w, for individual i is evolved according to:

14. 6. Updating Forecast Strategies: • Step 1-5 are repeated for 25 periods. • Figure 4: Timing of the market: • The fitness criterion : 25 50 ……………………….. 500

15. Evolution with individual “and” social learning

16. 3. ***Experiments*** • 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.

17. 3.1 ***Are intelligent agents rational?*** • Given a time horizon, can an economy with intelligent agents reach a rational-expectation equilibrium? Table 1: Summary Statistics

18. Results • 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.

19. 3.2 ***Which Level of Learning Dominates the Market?*** • 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?)

20. Data: • 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?

21. Model: (17) P(Choice=1|wealth) = • Standardize a variable, WEALTH. • The parameters, and, are estimated by the maximum likelihood method.

22. Analyses: • 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”.

23. **(Case 1)**: 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.

25. **(Case 1)**: 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.

27. Results • 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?

28. Conclusion • 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.