Learning without Recall from actions of neighbors

Under the Bayesian without Recall (BWR) model of inference, the agents behave rationally with respect to their most recent observations and yet they do not recall their history of past observations and cannot reason about how other agents are making their decisions. This model avoids the complexities of fully rational inference and also provides a behavioral foundation for non-Bayesian updating. We present the implications of the choice of signal and action space and utility structures for such agents, leading us to familiar update forms including the linear updates and the DeGroot model. We show that for a wide class of distributions from the exponential family with their conjugate priors, the BWR action updates take the form of a linear update in the self and neighboring actions. Furthermore, if the agents begin with noninformative priors then these action updates take the form of a convex combination as in the DeGroot model: agents who start from noninformative priors follow the DeGroot update and reach a consensus.