Large language models (LLMs) have been widely used as agents to complete different tasks, such as personal assistance or event planning. While most work has focused on cooperation and collaboration between agents, little work explores competition, another important mechanism that fosters the development of society and economy. In this paper, we seek to examine the competition behaviors in LLM-based agents. We first propose a general framework to study the competition between agents. Then, we implement a practical competitive environment using GPT-4 to simulate a virtual town with two types of agents, including restaurant agents and customer agents. Specifically, restaurant agents compete with each other to attract more customers, where the competition fosters them to transform, such as cultivating new operating strategies. The results of our experiments reveal several interesting findings ranging from social learning to Matthew Effect, which aligns well with existing sociological and economic theories. We believe that competition between agents deserves further investigation to help us understand society better. The code will be released soon.

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