Impact of Fake Agents on Information Cascades

In online markets, agents often learn from other's actions in addition to their private information. Such observational learning can lead to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">herding</i> or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">information cascades</i> 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fake agents</i> that take a fixed action in order to influence subsequent rational agents towards their preferred action. We characterize how the fraction of fake agents impacts the behavior of rational agents. 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. Our result shows a counter-intuitive phenomenon: there exist infinitely many scenarios where an increase in the fraction of fake agents 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.