Cooperation via sharing of probabilistic elements

Interactions of large societal groups exhibit predominantly a flat structure. It means that each member of the group has its aims, restricted perceiving, modelling, acting and evaluating abilities and interacts with a relatively small number of "neighbors". This is the fully scalable cooperation model worth of imitating. The paper introduces a formal model of this type with individual members being Bayesian decision makers who use so called fully probabilistic design of the optimal decision strategy. They are willing to cooperate with neighbors by providing them probabilistic distributions they use for their decision making (DM). At present research stage, interaction and communication structure are assumed to be given. Thus, the group DM is determined by specifying how the offered non-standard (probabilistic) fragmental information pieces should be exploited. The paper proposes a systematic procedure by formulating and solving the exploitation problem in a Bayesian way. Essentially, it: (i) takes the offered distributions as measured data; (ii) estimates an unknown global distribution describing the cooperating neighbors; (iii) projects this estimate on the domains of interest to the respective neighbors; (iv) approximate each projected distribution by the distribution, which has the form understandable to the decision maker. The proposed procedure, whose properties are illustrated by simple examples, is of independent interest since it can be used for model and aim elicitation.