Markovian Analysis of Information Cascades with Fake Agents

Abstract: People often learn from other's actions when they make decisions while doing online shopping. This kind of observational learning may lead to information cascades, which means agents might ignore their own signals and follow the 'trend' created collectively by the actions of their predecessors. It is well-known that with rational agents, such a cascade model can result in either correct or incorrect cascades. In this paper, we additionally consider the presence of fake agents who always take fixed actions and we investigate their influence on the outcome of these cascades. We propose an infinite Markov Chain sequence structure and a tree structure to analyze how the fraction and the type of such fake agents impacts behavior of the upcoming agents. We show that an increase in the fraction of fake agents may reduce the chances of their preferred outcome, and also there is a certain lower bound for the probability of a wrong cascade. In particular, we discuss the probability of an agent being fake tends to 1 and the effect of a constant portion of fake agents.