Large language models (LLMs) have been widely used as agents to complete different tasks, such as personal assistance or event planning. Although most of the work has focused on cooperation and collaboration between agents, little work explores competition, another important mechanism that promotes the development of society and economy. In this paper, we seek to examine the competition dynamics in LLM-based agents. We first propose a general framework for studying 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, the restaurant agents compete with each other to attract more customers, where competition encourages them to transform, such as cultivating new operating strategies. Simulation experiments reveal several interesting findings at the micro and macro levels, which align well with existing market and sociological theories. We hope that the framework and environment can be a promising testbed to study the competition that fosters understanding of society.