Asymptotic Consensus in the Model of Collective Decision Making in a Competitive Market

The paper considers the problem of reaching consensus in an oligopoly market in the absence of common knowledge among agents. The use of reflexive games and the indicative collective behavior model are the peculiarities of the approach to solve the problem. There is a brief overview of a number of consensus models with similar decision making structures. The object of study is the mutually affecting processes of the agents' actions dynamics in a Oournot oligopoly. The consensus model features for such a market are noted. It is shown that the asymptotic consensus is a static Nash equilibrium in the corresponding oligopoly game in normal form. The study also shows that the problem of reaching consensus yet has no complete analytical solution, even for the classical linear market model. There are no many applicable analytical results obtained for consensus models with similar structures. Only computational experiments can provide the answers to the question of convergence to consensus for many specific dynamics. There are analytical conclusions and results of numerical experiments for a number of practically important cases of the model that presented and discussed with illustrative examples in the study.