Continuous double auction (CDA) is one of the most popular price formation mechanisms in the financial markets. It is a continuous and repeated price formation process. CDA as a one-off game is well-researched. However, repeated CDA games present unexplored challenges due to their expansive solution space and complex equilibrium analysis. This study introduces a novel approach to model a trading day within the CDA framework as a repeated game, employing genetic algorithms (GA). In this context, chromosomes represent market participants. GA’s mechanisms—selection, crossover, and mutation—mimic key market learning processes such as communication, imitation, and experimentation. The study leverages best response dynamics to compute an approximate Nash equilibrium. This innovative application of GA in modeling game-theoretic CDA marks a significant advancement in addressing information asymmetry and bounded rationality among market players. The proposed methodology’s adaptability to a continuous-time framework underscores its potential applicability across diverse price discovery scenarios, where CDA is integral to market structure.