Gradio chatbot: how to export individual conversation histories?

Question

I'm working on a chatbot, that will later be used and tested in a psychological experiment. This is my first real programming project. I'm using the OpenAI API to provide the language model and Gradio for the UI. I want to add functionality, that would allow me export the conversations of each user, so that me and my team can them analyze later. I have some rough idea how this could be done, but need help with the specific implementation. This is the code I have so far, without the extra functionality:

from openai import OpenAI
import gradio as gr

client = OpenAI(
    api_key="OUR API KEY"
)

instructions = "OUR SYSTEM PROMPT"

def chat(system_prompt, user_prompt, model='gpt-4', temperature=0.0):
    response = client.chat.completions.create(
        temperature=temperature,
        model=model,
        messages=[
            {"role": "system", "content": system_prompt},
            {"role": "user", "content": user_prompt}
        ])

    res = response.choices[0].message.content
    return res


def format_chat_prompt(message, chat_history, max_convo_length):
    prompt = ""
    for turn in chat_history[-max_convo_length:]:
        user_message, bot_message = turn
        prompt = f"{prompt}\nUser: {user_message}\nAssistant: {bot_message}"
    prompt = f"{prompt}\nUser: {message}\nAssistant:"
    return prompt


def respond(message, chat_history, max_convo_length=1000000):
    formatted_prompt = format_chat_prompt(message, chat_history, max_convo_length)
    bot_message = chat(system_prompt=f'''{instructions}''',
                       user_prompt=formatted_prompt,
                       temperature=0.7,
                       )
    chat_history.append((message, bot_message))
    return "", chat_history


with gr.Blocks() as demo:
    chatbot = gr.Chatbot(height=300)
    msg = gr.Textbox(label="Prompt")
    btn = gr.Button("Submit")
    clear = gr.ClearButton(components=[msg, chatbot], value="Clear console")

    btn.click(respond, inputs=[msg, chatbot], outputs=[msg, chatbot])
    msg.submit(respond, inputs=[msg, chatbot], outputs=[msg, chatbot])  
gr.close_all()
demo.launch(share=True)

I have tried the following, which does create a txt file in the project directory:

from openai import OpenAI
import gradio as gr

client = OpenAI(
    api_key="OUR API KEY"
)

instructions = "OUR SYSTEM PROMPT"

def chat(system_prompt, user_prompt, model='gpt-4', temperature=0.0):
    response = client.chat.completions.create(
        temperature=temperature,
        model=model,
        messages=[
            {"role": "system", "content": system_prompt},
            {"role": "user", "content": user_prompt}
        ])

    res = response.choices[0].message.content
    return res


def format_chat_prompt(message, chat_history, max_convo_length):
    prompt = ""
    for turn in chat_history[-max_convo_length:]:
        user_message, bot_message = turn
        prompt = f"{prompt}\nUser: {user_message}\nAssistant: {bot_message}"
    prompt = f"{prompt}\nUser: {message}\nAssistant:"
    return prompt


def respond(message, chat_history, max_convo_length=1000000):
    formatted_prompt = format_chat_prompt(message, chat_history, max_convo_length)
    bot_message = chat(system_prompt=f"{instructions}", user_prompt=formatted_prompt, temperature=0.7)
    chat_history.append((message, bot_message))
    
    export_conversation(chat_history)

    return "", chat_history


def export_conversation(chat_history, filename="conversation.txt"):
    with open(filename, "w") as file:
        for turn in chat_history:
            user_message, bot_message = turn
            file.write(f"User: {user_message}\nAssistant: {bot_message}\n")


with gr.Blocks() as demo:
    chatbot = gr.Chatbot(height=300)
    msg = gr.Textbox(label="Prompt")
    btn = gr.Button("Submit")
    clear = gr.ClearButton(components=[msg, chatbot], value="Clear console")

    btn.click(respond, inputs=[msg, chatbot], outputs=[msg, chatbot])
    msg.submit(respond, inputs=[msg, chatbot], outputs=[msg, chatbot])  #press enter to submit
gr.close_all()
demo.launch(share=True)

The problem is that the txt file only contains the single most recent conversation of the user with the most recent input. It seems clear that I need some way to identify each user. Perhaps I could then create a dictionary with IDs as keys and individual conversations as values. What would be a good, easy-to-implement, way of going about the identification? And what other parts of the code would I need to adjust for it to work?