Is Ignoring Public Information Best Policy? Reinforcement Learning In Information Cascade

1. Artificial Economics 2006, Aalborg, Denmark, Sep. 14-15, 2006 Is Ignoring Public Information Best Policy?Reinforcement Learning In Information Cascade Toshiji Kawagoe Future University - Hakodate and Shinichi Sasaki Future University - Hakodate

2. Motivation • Dynamic extension of information cascade model • develop a new model featured by a reinforcement learning to extend the model of information cascade. • Examine the role of public information in correct guessing the true state of the world • conduct a series of simulations in order check which factor, public information or agent’s learning, is crucial to induce information cascade in a dynamic environment.

3. Model 1 • Information cascade • when it is optimal for each agent to ignore its private information and follow the decisions made by the other agents who have decided before. • The theory of information cascade was initiated by several researchers in economics and it has been tested in the laboratory with human subjects by a number of experimental economists

4. Model 2 • Each agent • makes a decision sequentially one by one. • tries to predict the true state of the world. • knows prior probability distribution of the state of the world. • receives a noisy signal of the state of the world privately. • also knows likelihood of receiving that noisy signal conditional on the state. • observes publicly announced past decisions made by the other agents (public information).

6. Theoretical Prediction • Each agent can calculate posterior probability of the realized state of world by utilizing its private information, likelihood and public information to predict true state of the world. • But if a small number of agents accidentally made same decisions, then it is easily shown by Bayes rule that an agent who observes such public information should ignore its private information and follows its predecessors’ decisions.

7. Good and Bad Cascade • Good cascade • If the prediction made by agents who are involved in an information cascade is true state of the world. • Bad cascade • The prediction made by agents who are involved in an information cascade is not correct state of the world.

8. Symmetric condition • Prior probability of the state A and B • p(A) = p(B) = ½ • Likelihood of receiving a signal a (b) in the state A (B) • p(a|A) = p(b|B) = 2/3 • At least two agents make same prediction, an agent who observes such public information follows the predecessors’ prediction.

9. Asymmetric condition • Prior probability of the state A and B • p(A) = p(B) = ½ • Likelihood of receiving a signal a (b) in the state A (B) • p(a|A) = 6/7 p(b|B) = 2/7 • If at least four agents predict A, then predicting A is best response for an agent who observes such public information, and if at least an agent predict B, then predicting B is best response for subsequent agents whatever signal they receive.

10. Three types of agent • Type B • Agents who follows Bayes rule. • Type RNP • Agents who follow reinforcement learning without public information • Type RP • Agents who follow reinforcement learning with public information

11. Frequency of information cascade in symmetric case

12. Frequency of information cascade in asymmetric case

13. RP model Updating rule if agent i predicts A and it is correct (incorrect) at period t. otherwise Probability of predicting A

17. Conclusion 1 • Previous studies reported that agents’ behaviors were still affected by their private signals even after a longer cascade has already occurred. • We tried to answer that question by developing a new model featured by a reinforcement learning to extend the model of information cascade.

18. Conclusion 2 • Our results showed that • incorporating agent’s past experience of prediction had great impact on the emergence of information cascade • providing public information was rather detrimental for agents who would like to predict correct state of the world • So, ignoring public information, and believing one’s own private information and experiences is much better for making correct prediction.