On decision making in tandem networks

Abstract

We study the convergence of Bayesian learning in a tandem social network. Each agent receives a noisy signal about the underlying state of the world, and observes her predecessor's action before choosing her own. We characterize the conditions under which, as the network grows larger, agents' beliefs converge to the true state of the world. The literature has predominantly focused on the case where the number of possible actions is equal to that of alternative states. We examine the case where agents pick three-valued actions to learn one of two possible states of the world. We focus on myopic strategies, and distinguish between learning in probability and learning almost surely. We show that ternary actions are not sufficient to achieve learning (almost sure or in probability) when the likelihood ratios of the private signals are bounded. When the private signals can be arbitrarily informative (unbounded likelihood ratios), we show that there is learning, in probability. Finally, we report an experimental test of how individuals learn from the behavior of others. We explore sequential decision making in a game of three players, where each decision maker observes her immediate predecessor's binary or ternary action. Our experimental design uses Amazon Mechanical Turk, and is based on a setup with continuous signals, discrete actions and a cutoff elicitation technique introduced in [QK05). We replicate the findings of the experimental economics literature on observational learning in the binary action case and use them as a benchmark. We find that herds are less frequent when subjects use three actions instead of two. In addition, our results suggest that with ternary actions, behavior in the laboratory is less consistent with the predictions of Bayesian behavior than with binary actions.