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Understanding Stock Market Boom and Bust: Insights from Minority and Majority Games

This analysis by Isavella Kapitani and Yuxiu Hu explores endogenous boom and bust phenomena in stock markets, drawing on insights from Brian Arthur's contrarian game theory. The study employs a simulator to illustrate how agents behave in minority and majority scenarios, revealing that to succeed in the stock market, one must learn from different types of advisors. It emphasizes the importance of memory and decision-making based on past forecasts and neighbor influences, highlighting strategies for navigating market dynamics effectively.

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Understanding Stock Market Boom and Bust: Insights from Minority and Majority Games

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  1. BOOM AND MUSTHERDING AND LEARNING FROM GURUs By : IsavellaKapitani and Yuxiu Hu

  2. What Causes Endogenous Boom and Bust in Stock Markets? • Brian Arthur from Santa Fe(1977) institute stock market game. • He says it is a contrarian or minority game for which there is NO HOMOGENOUS RATIONAL EXPECTATIONS. • SO TO WIN WHEN IN A MINORITY, AGENTS HAVE TO ENDOGENOUSLY BREAK AWAY FROM GROWING PRICE TREND. • TO TEST THIS, A SIMPLE SIMULATOR IS DONE: • PAY OFF FUNCTION PICKS WINNERS: • WHO ARE IN MINORITY • WHO ARE IN MAJORITY • WHO ARE RANDOM WHAT DO WE FIND?

  3. Win a stock game No unique algorithm/optimal strategy Reason: Price determination is Self-Reflexive, ()) ( based on believes)(based on reality) Strategies Modifying believes

  4. Then how to win a stock market game?learn from ‘Guru’ in the market. How to Learn from “Guru”? learn neighbors who have memory • In majority game, mimic from advisors who have long term memory; • In minority game, gain advices from advisors who have zero memory; • however, in random game, there is no definite rule to find the appropriate advisors.

  5. Testing and winner determination function: • Step 1: Individual forecast: • Each agent calculates its forecast based on its own past. • Mi () number of decisions and outcomes as follows: • The forecast fi,t+1 can take a value in the range [-1,+1], • where fi,t+1 >0 recommendation to buy, • fi,t+1 < 0 recommendation to sell, and • fi,t+1= 0 random recommendation. • Step 2: Decision: • The decision of an agent is based on a weighted sum of forecasts that its neighbours give it and its own. Zero-memory agents give advice based on random basis. • Majority agents win when the price is falling or increasing in a steady rate. • Minority agents win when the price if fluctuating and they represent the loop and behave differently from the majority of the agents. • Random agents win in both of the above cases.

  6. Comparison of statistics

  7. Degree of memory MAJORITY WINS: GURU IN THE CENTER OF NETWORK HAVE HIGHEST MEMORY 2) MINORITY WINS: GURU IN THE CENTER OF NETWORK HAVE ZERO MEMORY 3) RANDOM WINS: NO STRUCTURE

  8. Network Statistics 1)MAJORITY WINS: MORE AGENTS HAVE MORE MEMORY SINCE THE FOLLOW GURUS 3)RANDOM WINS: AGENTS BEHAVE RANDOMLY 2)MINORITY WINS: FAT TAIL, AGENTS HAVE ZERO MEMORY

  9. Price trend MA J O R I T Y When majority wins the price is increasing or decreasing. In this case is decreasing since everyone is buying. M I N O R I T Y When minority wins we experience boom and bust in price. The price is fluctuating but not is a stable rate as in the minority case. R A N D O M

  10. Network Statistics Minority: most of the agents are sellers. There are a few buyers as well. Majority: most of the agents are buyers. There are a few that are selling as well. = buyers =sellers Random: almost all of the agents are selling.

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