Who pays for custom GPT usage?

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Does publicly sharing a GPTs incur additional charges?

A GPT operates in someone’s plus account, so any language model inference charges are borne by OpenAI for operating ChatGPT Plus. If the GPT has actions and makes calls to your API plugin, then you get the minimal data and hosting requirement of servicing the API request of the action on your domain. If your API has features powered by AI on demand, then you could be footing the bill yourself for providing AI-enhanced services.