Markovian Analysis of Information Cascades with Fake Agents

TL;DR

The paper addresses how fake agents influence information cascades in Bayesian sequential decision making. It develops an infinite Markov chain model for history through the statistic $h_n$ and introduces two analytic tools—a tree-structure approximation and a sequence-structure bound—to quantify cascade probabilities under fake-agent fractions $\epsilon$ and $\beta$. Key results show that increasing fake-agent presence can reduce the probability of a wrong cascade, but there are explicit Bayesian thresholds $\epsilon_r$ and cascade dynamics that can induce discontinuities; in the limit $\gamma=\epsilon+\beta\to1$, the information content of observations diminishes and cascades become dominated by past actions. The work provides practical methods to bound cascades and suggests future directions for analyzing non-Bayesian rational networks and scenarios with small fake-agent fractions.

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.

Figures (11)

• Figure 1: The Binary Symmetric Chnnel though which agents receive signals
• Figure 2: Transition Diagram of the Random Walk
• Figure 3: Probability of Y Cascade as a function of $\epsilon$ for V=B, p=0.7 and $\beta=0$, $\beta=0.05$
• Figure 4: Probability of Y Cascade as a function of $\epsilon$ for V=B and p=0.7 with different $\beta$
• Figure 5: Bayesian Thresholds