Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Impact of Fake Agents on Information Cascades

Pawan Poojary, Randall Berry

TL;DR

This work analyzes Bayesian information cascades when sequential rational agents face random fake agents that fix a fixed action. It develops a countably infinite-state Markov chain model with a compact recursive method to compute cascade probabilities and agent welfare, revealing infinitely many $oldsymbol{\e}$-thresholds where small increases in fake agents can reduce the fake’s favored cascade while markedly boosting rational welfare. The results show abrupt welfare gains at these thresholds and provide insights into platform interventions (co-ordinator) that can further improve learning under realistic manipulation. The findings hold under general priors and zero ex-ante payoff, with extensions to non-zero ex-ante payoffs and various coordinator schemes, highlighting fundamental trade-offs in manipulation, learning, and welfare in sequential decision settings.

Abstract

In online markets, agents often learn from other's actions in addition to their private information. Such observational learning can lead to herding or information cascades in which agents eventually ignore their private information and "follow the crowd". Models for such cascades have been well studied for Bayes-rational agents that arrive sequentially and choose pay-off optimal actions. This paper additionally considers the presence of fake agents that take a fixed action in order to influence subsequent rational agents towards their preferred action. We characterize how the fraction of such fake agents impacts the behavior of rational agents given a fixed quality of private information. Our model results in a Markov chain with a countably infinite state space, for which we give an iterative method to compute an agent's chances of herding and its welfare (expected pay-off). Our main result shows a counter-intuitive phenomenon: there exist infinitely many scenarios where an increase in the fraction of fake agents in fact reduces the chances of their preferred outcome. Moreover, this increase causes a significant improvement in the welfare of every rational agent. Hence, this increase is not only counter-productive for the fake agents but is also beneficial to the rational agents.

Impact of Fake Agents on Information Cascades

TL;DR

This work analyzes Bayesian information cascades when sequential rational agents face random fake agents that fix a fixed action. It develops a countably infinite-state Markov chain model with a compact recursive method to compute cascade probabilities and agent welfare, revealing infinitely many -thresholds where small increases in fake agents can reduce the fake’s favored cascade while markedly boosting rational welfare. The results show abrupt welfare gains at these thresholds and provide insights into platform interventions (co-ordinator) that can further improve learning under realistic manipulation. The findings hold under general priors and zero ex-ante payoff, with extensions to non-zero ex-ante payoffs and various coordinator schemes, highlighting fundamental trade-offs in manipulation, learning, and welfare in sequential decision settings.

Abstract

In online markets, agents often learn from other's actions in addition to their private information. Such observational learning can lead to herding or information cascades in which agents eventually ignore their private information and "follow the crowd". Models for such cascades have been well studied for Bayes-rational agents that arrive sequentially and choose pay-off optimal actions. This paper additionally considers the presence of fake agents that take a fixed action in order to influence subsequent rational agents towards their preferred action. We characterize how the fraction of such fake agents impacts the behavior of rational agents given a fixed quality of private information. Our model results in a Markov chain with a countably infinite state space, for which we give an iterative method to compute an agent's chances of herding and its welfare (expected pay-off). Our main result shows a counter-intuitive phenomenon: there exist infinitely many scenarios where an increase in the fraction of fake agents in fact reduces the chances of their preferred outcome. Moreover, this increase causes a significant improvement in the welfare of every rational agent. Hence, this increase is not only counter-productive for the fake agents but is also beneficial to the rational agents.

Paper Structure

This paper contains 24 sections, 9 theorems, 79 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Related Work
  4. Organisation
  5. Model
  6. Optimal decision, cascades and welfare
  7. Markovian Analysis of Cascades
  8. Error thresholds
  9. $\bm{Y}$ cascade probability, $\bm{\mathbb{P}_{Y\text{-cas}}}$
  10. Quantifying the abrupt changes in $\bm{\mathbb{P}_{Y\text{-cas}}}$ at error thresholds
  11. Effect of fake agents on $\bm{\mathbb{P}_{Y\text{-cas}}}$ at low values of $\bm{\epsilon$
  12. Probability of cascades for finite agent arrivals
  13. Welfare for ordinary agents
  14. Learning in the limit
  15. Effects of a Platform Co-ordinator
  16. ...and 9 more sections

Key Result

Lemma 1

Agent $n$ cascades to a $Y \, (N)$ if and only if $l_{n-1} < \frac{1-p}{p}$$( l_{n-1} > \frac{p}{1-p} )$ and otherwise follows its private signal $S_n$.

Figures (13)

  • Figure 1: $(a)$ The BSC through which agents receive private signals. $(b)$ The channel through which agents' actions are corrupted.
  • Figure 2: Partial transition diagram of random walk $\{h_n\}$ given $V$.
  • Figure 3: Thresholds $\epsilon_r$ for the indicated values of $r$ versus $p$.
  • Figure 4: An enumeration of all possible sequences that would lead to a $Y$ cascade. The term $Y^{t}$ represents a sequence of $t$ consecutive $Y$'s. The sequence $\{r_n \}$ is defined as per \ref{['r_updates']}.
  • Figure 5: Probability of $Y$ cascade as a function of $\epsilon$ for $V=B$ and $p=0.7$.
  • ...and 8 more figures

Theorems & Definitions (11)

  • Definition 1
  • Lemma 1
  • Lemma 2
  • Remark 1
  • Theorem 1
  • Lemma 3
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Lemma 4
  • ...and 1 more