The emergence of large language models (LLMs) has significantly advanced the simulation of believable interactive agents. However, the substantial cost on maintaining the prolonged agent interactions poses challenge over the deployment of believable LLM-based agents. Therefore, in this paper, we develop Affordable Generative Agents (AGA), a framework for enabling the generation of believable and low-cost interactions on both agent-environment and inter-agents levels. Specifically, for agent-environment interactions, we substitute repetitive LLM inferences with learned policies; while for inter-agent interactions, we model the social relationships between agents and compress auxiliary dialogue information. Extensive experiments on multiple environments show the effectiveness and efficiency of our proposed framework. Also, we delve into the mechanisms of emergent believable behaviors lying in LLM agents, demonstrating that agents can only generate finite behaviors in fixed environments, based upon which, we understand ways to facilitate emergent interaction behaviors. Our code is publicly available at: https://github.com/AffordableGenerativeAgents/Affordable-Generative-Agents.