This paper investigates a closed loop supply chain (CLSC) encompassing a manufacturer, a retailer, and consumers operating within the carbon trading scheme. Employing the focus theory of choice, we analyze the decision-making processes of the retailer, considering various personality traits. A Stackelberg game is formulated, wherein the manufacturer assumes responsibility for recycling activities. The research explores the impact of the retailer’s optimism and confidence levels on optimal decision-making within a positive evaluation system. Numerical examples are employed to elucidate equilibrium solutions, illustrating the correlation between the retailer’s personality traits and the manufacturer’s optimal decisions. Furthermore, a sensitivity analysis is conducted on the carbon trading price and the manufacturer’s carbon emission quota allocation within a single cycle under the carbon trading scheme. The investigation concludes with an examination of the influence of recycling prices on the manufacturer’s optimal revenue. The findings indicate that retailers with distinct personality traits adopt varied pricing strategies. Decreases in optimism and self-confidence levels prompt the retailer to opt for relatively lower retail profit pricing. Simultaneously, the manufacturer demonstrates a preference for collaborating with a retailer characterized by optimism and lower confidence levels, thereby enhancing overall manufacturing revenue. Notably, under the carbon trading scheme, fluctuations in carbon trading and recycling prices distinctly influence the manufacturer’s decisions.