This paper investigates the emergent social dynamics of Large-Scale Language Model (LLM) agents in the spatially extended El Farol Bar problem. We observe how LLM agents autonomously navigate this classic social dilemma. We find that LLM agents generate spontaneous motivations to go to the bar and alter their decision-making by forming groups. Furthermore, we observe that LLM agents fail to fully solve the problem, but rather behave in a human-like manner. These results reveal a complex interplay between extrinsic incentives (constraints specified by prompts, such as the 60% threshold) and intrinsic incentives (culturally encoded social preferences derived from pre-training), demonstrating that LLM agents naturally balance formal game-theoretic rationality with the social motivations that characterize human behavior. These results suggest that LLM agents can realize novel models of collective decision-making that were previously unfeasible in game-theoretic problem settings.