  Behavior study experiments are an important part of society modeling and
understanding human interactions. In practice, many behavioral experiments
encounter challenges related to internal and external validity,
reproducibility, and social bias due to the complexity of social interactions
and cooperation in human user studies. Recent advances in Large Language Models
(LLMs) have provided researchers with a new promising tool for the simulation
of human behavior. However, existing LLM-based simulations operate under the
unproven hypothesis that LLM agents behave similarly to humans as well as
ignore a crucial factor in human decision-making: emotions.
  In this paper, we introduce a novel methodology and the framework to study
both, the decision-making of LLMs and their alignment with human behavior under
emotional states. Experiments with GPT-3.5 and GPT-4 on four games from two
different classes of behavioral game theory showed that emotions profoundly
impact the performance of LLMs, leading to the development of more optimal
strategies. While there is a strong alignment between the behavioral responses
of GPT-3.5 and human participants, particularly evident in bargaining games,
GPT-4 exhibits consistent behavior, ignoring induced emotions for rationality
decisions. Surprisingly, emotional prompting, particularly with `anger'
emotion, can disrupt the "superhuman" alignment of GPT-4, resembling human
emotional responses.
