This paper proposes a study measuring regret using benchmarks from online learning and game theory to quantitatively evaluate the decision-making ability of LLM-based autonomous agents. In particular, we analyze the performance of LLM agents in a multi-agent environment where they interact with each other. We empirically investigate the no-regret behavior of LLM, provide theoretical insights, and identify cases where advanced LLMs, such as GPT-4, fail to achieve no-regret. Furthermore, we propose a novel regret loss (regret-loss) that does not require (optimal) action labels, establish generalization guarantees, and demonstrate its potential for leading to no-regret learning algorithms. We verify the effectiveness of the proposed regret loss through experiments.