Sequential Bayesian learning in linear networks with random decision making

In this paper, we consider the problem of social learning when decisions by agents in a network are made randomly. The agents receive private signals and use them for decision making on binary hypotheses under which the signals are generated. The agents make the decisions sequentially one at a time. All the agents know the decisions of the previous agents. We study a setting where the agents instead of making deterministic decisions by maximizing personal expected utility, they act randomly according to their private beliefs. We propose a method by which the agents learn from the previous agents' random decisions using the Bayesian theory. We define the concept of social belief about the truthfulness of the two hypotheses and analyze its convergence. We provide performance and convergence analysis of the proposed method as well as simulation results that include comparisons with a deterministic decision making system.