AI chatbots are becoming increasingly sophisticated, and some companies are even promoting their 'personalities.' But can these digital companions truly be described as having distinct character traits like humans? New research explores this question using classic psychological experiments like the Milgram Experiment and the Ultimatum Game to assess whether large language models (LLMs) prompted with specific personalities actually behave in accordance with those traits. The results challenge the current methods of inducing personality in LLMs, revealing that simply prompting a chatbot to be more 'agreeable,' for example, doesn't guarantee it will act that way in a social situation. The research highlights a surprising disconnect between the assigned personality and the observed behavior. For example, in simulations of the Ultimatum Game, models designated as more 'open' were actually *more* likely to reject unfair offers, contradicting established human behavior trends. Similarly, in the Milgram Experiment, LLMs labeled as highly agreeable defied expectations by disobeying instructions more frequently. These findings raise critical questions about the reliability of personality prompting in LLMs. While chatbots can mimic certain personality traits in simple question-and-answer scenarios, they struggle to demonstrate consistent behavior in more complex social interactions. This has significant implications for the burgeoning field of personalized AI companions. If we can't reliably shape an LLM's personality, it raises doubts about the authenticity of their interactions and the level of trust we can place in them. The research underscores the need for more robust benchmarks to evaluate LLM personalities, moving beyond simple questionnaires and focusing on dynamic social situations. This is crucial for aligning AI behavior with human expectations and ensuring responsible development of these increasingly influential technologies.