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You basically need the person that's paying you to stop paying you when it stops being open. You need the value they receive to evaporate when you close the graph off. Once you have the graph, you hold the value and can extract any rent you choose to.
I think you need others to have the graph and ideally many of them. If you can incentivize competitors to also serve the graph, that'd prevent any one company from successfully extorting customers.
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I do agree that the business model in itself is not sufficient to guarantee the graph remains open. This idea is work in progress and I am open to suggestions. My high-level thinking is this:
I'm trying to figure out how to structure the product and the business model in such a way that the most value for shareholders is created when the graph remains open.