Open complex systems such as financial markets evolve in highly dynamic and uncertain environments. They are often subject to significant fluctuations due to unanticipated behaviours and information. Modelling and simulating these systems by means of multi-agent systems, i.e., through artificial markets is a valuable approach. Initial Public Offering (IPO) is a process based on finding a reasonable offering price or the price of the first assets sale by a firm to public. The study of the firms' strategic choices at the IPO requires the use of formal tools like game theory. This article is about the study, analysis and simulation of a firm's dynamic evolution at IPO using the EGT (Evolutionary Game Theory) as a formal framework for IPO strategies (offering prices) through modeling a financial market by multi-agent system. The firm in the system is a cognitive agent built around a classifier system. Simulations with our prototype allow us to deduce the factors that cause IPO under pricing.