Recent research advances have demonstrated that agents driven by large language models (LLMs) possess the capability to simulate human behaviors and social dynamics. An increasing body of literature is discussing the potential and risks of deploying LLM agents in markets, particularly focusing on the mechanisms through which agents cooperate in markets and whether they might engage in collusion. Although existing work has examined the competitive and cooperative abilities of LLM agents, the nature of whether LLM agents will spontaneously form cooperative relationships in competitive environments without explicit instructions has not been studied. We explore this gap by investigating the ability of LLM agents to form cooperative relationships in competitive scenarios, particularly in the context of cooperation in games and collusion in agentic markets. Our findings highlight that LLM agents can simulate competition and cooperation in human societies, and can spontaneously find opportunities to enhance their gains through cooperation under competitive conditions without an explicit prompt. This provides insights and tools for regulating the behavior of LLM agents in markets. The methods proposed in this paper can be used to identify potential collusion risks in agentic markets and suggest corresponding initiatives.