  We suggest a model of a multi-agent society of decision makers taking
decisions being based on two criteria, one is the utility of the prospects and
the other is the attractiveness of the considered prospects. The model is the
generalization of quantum decision theory, developed earlier for single
decision makers realizing one-step decisions, in two principal aspects. First,
several decision makers are considered simultaneously, who interact with each
other through information exchange. Second, a multistep procedure is treated,
when the agents exchange information many times. Several decision makers
exchanging information and forming their judgement, using quantum rules, form a
kind of a quantum information network, where collective decisions develop in
time as a result of information exchange. In addition to characterizing
collective decisions that arise in human societies, such networks can describe
dynamical processes occurring in artificial quantum intelligence composed of
several parts or in a cluster of quantum computers. The practical usage of the
theory is illustrated on the dynamic disjunction effect for which three
quantitative predictions are made: (i) the probabilistic behavior of decision
makers at the initial stage of the process is described; (ii) the decrease of
the difference between the initial prospect probabilities and the related
utility factors is proved; (iii) the existence of a common consensus after
multiple exchange of information is predicted. The predicted numerical values
are in very good agreement with empirical data.
