TY - GEN
T1 - Bayesian Learning with Random Arrivals
AU - Le, Tho Ngoc
AU - Subramanian, Vijay G.
AU - Berry, Randall A.
N1 - Publisher Copyright:
© 2018 IEEE.
PY - 2018/8/15
Y1 - 2018/8/15
N2 - We add to a line of work considering the impact of observation imperfections in models of Bayesian observational learning. In particular, we study a discrete-time model in which in each time-slot, an agent may randomly arrive. Agents who arrive have the opportunity to buy a given item. If an agent chooses to buy, this action is recorded for subsequent agents. However, the decisions of agents that choose not to buy are not recorded. Hence, if no one buys in a given slot, agents are unaware if this was due to no agent arriving or an agent choosing not to buy. We study the impact of this uncertainty on the emergence of information cascades. Using a Markov chain based analysis, we show that the probability of incorrect cascades and the expected time until a cascade happens are not monotonic in the arrival probability of a user. We find that adding a small uncertainty in the arrival information from the perfect information setting will make a buy cascade happen with higher probability than a not-buy cascade. However, if the agents' private signals are weak, then a not-buy cascade is more likely to occur for most arrival rates, resulting in wrong cascades dominating when the item is good and vice-versa when the item is bad.
AB - We add to a line of work considering the impact of observation imperfections in models of Bayesian observational learning. In particular, we study a discrete-time model in which in each time-slot, an agent may randomly arrive. Agents who arrive have the opportunity to buy a given item. If an agent chooses to buy, this action is recorded for subsequent agents. However, the decisions of agents that choose not to buy are not recorded. Hence, if no one buys in a given slot, agents are unaware if this was due to no agent arriving or an agent choosing not to buy. We study the impact of this uncertainty on the emergence of information cascades. Using a Markov chain based analysis, we show that the probability of incorrect cascades and the expected time until a cascade happens are not monotonic in the arrival probability of a user. We find that adding a small uncertainty in the arrival information from the perfect information setting will make a buy cascade happen with higher probability than a not-buy cascade. However, if the agents' private signals are weak, then a not-buy cascade is more likely to occur for most arrival rates, resulting in wrong cascades dominating when the item is good and vice-versa when the item is bad.
UR - http://www.scopus.com/inward/record.url?scp=85052468023&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85052468023&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2018.8437317
DO - 10.1109/ISIT.2018.8437317
M3 - Conference contribution
AN - SCOPUS:85052468023
SN - 9781538647806
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 926
EP - 930
BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 IEEE International Symposium on Information Theory, ISIT 2018
Y2 - 17 June 2018 through 22 June 2018
ER -