As large language models (LLMs) become increasingly capable of autonomous decision-making, they introduce new challenges and opportunities for human-AI cooperation in mixed-motive contexts. While prior research has primarily examined AI in assistive or cooperative roles, little is known about how humans interact with AI agents perceived as independent and strategic actors. This study investigates human cooperative attitudes and behaviors toward LLM agents by engaging 30 participants (15 males, 15 females) in repeated Prisoner's Dilemma games with agents differing in declared identity: purported human, rule-based AI, and LLM agent. Behavioral metrics, including cooperation rate, decision latency, unsolicited cooperative acts and trust restoration tolerance, were analyzed to assess the influence of agent identity and participant gender. Results revealed significant effects of declared agent identity on most cooperation-related behaviors, along with notable gender differences in decision latency. Furthermore, qualitative responses suggest that these behavioral differences were shaped by participants interpretations and expectations of the agents. These findings contribute to our understanding of human adaptation in competitive cooperation with autonomous agents and underscore the importance of agent framing in shaping effective and ethical human-AI interaction.