(eng): Bayesian decision making (DM) quantifies information by the probability density (pd) of treated variables. Gradual accumulation of information during acting increases the DM quality reachable by an agent exploiting it. The inspected accumulation way uses a parametric model forecasting observable DM outcomes and updates the posterior pd of its unknown parameter. In the thought multi-agent case, a neighbouring agent, moreover, provides a privately-designed pd forecasting the same observation. This pd may notably enrich the information of the focal agent. Bayes' rule is a unique deductive tool for a lossless compression of the information brought by the observations. It does not suit to processing of the forecasting pd. The paper extends solutions of this case. It: a) refines the Bayes'-rule-like use of the neighbour's forecasting pd. b) deductively complements former solutions so that the learnable neighbour's reliability can be taken into account. c) specialises the result to the exponential family, which shows the high potential of this information processing. d) cares about exploiting population statistics.