This paper presents a novel method for interpreting value trade-offs between conflicting goals (e.g., honesty and consideration for the other party's feelings) in large-scale language models (LLMs). Using the 'cognitive model' from cognitive science, we evaluate the extent to which LLMs reflect human-like value trade-offs. We analyze the inference effort and training dynamics after reinforcement learning in two settings: a state-of-the-art black-box model and an open-source model, revealing patterns between informational utility and social utility. The results show that informational utility is higher than social utility in the inference model, and this trend is also confirmed in the open-source model with high mathematical inference ability. In addition, through the analysis of the training dynamics of LLMs, we find large changes in the utility value in the early training stage and the persistent influence of the base model and the selection of pre-training data. This method can be applied to various development situations of LLMs, and can contribute to forming hypotheses about high-dimensional behaviors, improving the training system of inference models, and improving the control of value trade-offs during model training.