Social learning with heterogeneous agents and sequential decision making

In this paper, we consider the problem of social learning in a network of agents where the agents make decisions sequentially by choosing one of two hypotheses on the state of nature. Each agent observes a signal generated according to one of the hypotheses and knows the decisions of all the previous agents in the network. The network contains two types of agents: rational and irrational. A rational agent makes a decision by not only using its private observation but also the decisions of each of the agents which already made decisions. To that end, the agent employs Bayesian theory. An irrational agent makes a decision by ignoring the available information and by randomly choosing the hypothesis. We analyze the asymptotic performance of a system with rational and irrational agents where we study rational agents that use either a deterministic or random decision making policies. We propose a specific random decision making policy that is based on the social belief and the private signals of the agents. We prove that under mild conditions the expected social belief in the true state of nature tends to one if the rational agents use the proposed random policy. In a network with rational agents that use deterministic policy, the conditions for convergence are stricter. We provide simulation results on the studied systems and compare their performance.