This study investigates how the Big Five personality traits influence decision-making processes in AI agents within public spaces. Using AgentVerse framework and GPT-3.5-turbo, we simulated interactions among 10 AI agents, each embodying different dimensions of the Big Five personality traits, in a classroom environment responding to misinformation. The experiment assessed both public expressions ([Speak]) and private thoughts ([Think]) of agents, revealing significant correlations between personality traits and decision-making patterns. Results demonstrate that Openness to Experience had the strongest impact on information acceptance, with curious agents showing high acceptance rates and cautious agents displaying strong skepticism. Extraversion and Conscientiousness also showed notable influence on decision-making, while Neuroticism and Agreeableness exhibited more balanced responses. Additionally, we observed significant discrepancies between public expressions and private thoughts, particularly in agents with friendly and extroverted personalities, suggesting that social context influences decision-making behavior. Our findings contribute to understanding how personality traits shape AI agent behavior in social settings and have implications for developing more nuanced and context-aware AI systems.