<p>This paper introduces an inertial subgradient-type algorithm for solving equilibrium problems with strong monotonicity, constrained over the fixed point set of a nonexpansive mapping in the framework of a real Hilbert space. The proposed method integrates inertial and subgradient strategies to enhance convergence properties while avoiding the computational challenges of metric projections onto complex sets. A strong convergence theorem is established under appropriate constraint qualifications for the scalar sequences. Numerical experiments in both finite and infinite dimensional settings, including applications to Nash–Cournot oligopolistic market equilibrium models, highlight the efficacy and computational advantages of the algorithm. These results demonstrate the potential for broader applications in optimization and variational analysis.</p>