To address the coordination issue of connected autonomous vehicles (CAVs) at unsignalized intersections, this paper proposes a game-theory-based distributed strategy equalization algorithm. To begin, the vehicles present in the scene are conceptualized as participants in a game theory. The decision-payoff function takes into account three critical performance indicators: driving safety, driving comfort, and driving efficiency. Then, virtual logic lines connect the front and rear extremities of vehicles with odd and even numbers at the intersection to create a virtual logic ring. By dividing the virtual logic ring into numerous overlapping game groups, CAVs can engage in negotiation and interaction within their respective game groups. This enables the revision of action strategies and facilitates interaction between the overlapping game groups. A further application of the genetic algorithm (GA) is the search for the optimal set of strategies in constrained multi-objective optimization problems. The proposed decision algorithm is ultimately assessed and certified through a collaborative simulation utilizing Python and SUMO. In comparison to the first-come, first-served algorithm and the cooperative driving model based on cooperative games, the average passing delay is decreased by 40.7% and 6.17%, respectively, resulting in an overall improvement in the traffic system’s passing efficiency.