How to exploit external model of data for parameter estimation?

Any cooperation in multiple-participant decision making (DM) relies on an exchange of individual knowledge pieces and aims. A general methodology of their rational exploitation without calling for an objective mediator is still missing. Desired methodology is proposed for an important particular case, when a participant, performing Bayesian parameter estimation, is offered a model relating the observable data to their past history. The designed solution is based on the so-called fully probabilistic design (FPD) of DM strategies. The result reduces to an 'ordinary' Bayesian estimation if the offered model is the sample probability density function (pdf), i.e. if it provides additional observations.