<p>Employer branding involves strategies to create a positive corporate image, attracting and retaining high-quality workers. However, the impact of these policies on employees remains unclear in existing literature. In this study, drawing from econophysics literature—particularly the Maxwell–Boltzmann distribution—we use an evolutionary game theory model to investigate the population exposure to these strategies. Through agent-based methods, we analyze two-player populations seeking an optimal equilibrium, exploring the influence of wage offers and employee consumption levels. Additionally, we consider external sponsors, like relatives or universal income providers, who can subsidize wages. Our findings indicate the significant role of external sponsors in game dynamics, prompting their consideration in human resources management.</p>