The volatility of stock prices is difficult to explain within the confines of rational pricing models. Changes in prices have become permanent at both the individual and the aggregate level. Therefore, when keeping the hypothesis of a rational behavior of agents, we need to give a new explanation to the price settlement of financial assets at any moment of time. In a model based on an original mathematical framework, we introduce persistent time-varying prices resulting from rational strategic interactions of agents. We demonstrate that in a close to equilibrium market, actual prices give the best approximation of fundamental value; We also explain why, in some circumstances, rational behavior may lead to the development of a bubble or the surge of a financial crisis.