Is Apple paying OpenAI, or vice versa?

I do not know.  Am I wrong to think that in optimal contracts theory there should be payments going in both directions, as there is a dual agency relationship?  Of course optimal contracts theory often fails.

Ben Thompson has a hypothesis (gated):

This sounds like a play to acquire users and mindshare, with the potential of upselling those users to a subscription, i.e. the exact same model that OpenAI has on their website and apps. Moreover, if this partnership entails Apple not paying, it also explains why OpenAI is the only option to start: Google, for example, probably wanted to be paid for Gemini, or Anthropic for Claude, and I can imagine (1) Apple holding the line on not paying, particularly if (2) OpenAI is making an aggressive move to build out its consumer business and be a durable brand and winner in the consumer space. In short, my updated current thinking is that both Apple and OpenAI are making the bet that very large language models are becoming increasingly commoditized, which means that Apple doesn’t have to pay to get access to one, and OpenAI sees scale and consumer mindshare as the best route to a sustainable business.

If I had to guess, I would think the main payment goes from Apple to OpenAI?  We know Apple is very, very good at extracting revenue from customers.  OpenAI, no matter how rapid its growth path over the next few years, simply cannot have a comparable record.  There is thus one model where Apple pays for AI access rights, and later on then charges more for iPhones.  You still will be able to buy cheaper phones without these services, if enough people demand that.  OpenAI of course will be charging you as well, but only if you go over quota, as they face the “extra subscription fatigue issue” in a way that Apple does not.

Just a hypothesis.  The fact that we do not know should tell you something about the limits of economic reasoning.