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This is the TCP backoff algorithm, specifically the slow start to find the optimal bandwidth. In your analogy, it would find the optimal amount that a person is willing to reciprocate.

Not only does this algorithm exist, but we're using it to communicate right now!

https://en.wikipedia.org/wiki/TCP_congestion_control

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I have noticed this algorithm in many places which is why I think it is a missing piece in game theory and why formalizing it could be powerful. People use this instinctively in their interactions with others and algorithms (like the one you pointed out) have been created using the basic concept so a formalization of the math is likely in order. Consider the question of how big the offering should be. What if all parties are actually getting the optimum result, what mechanism stops the increase/why? Does it stop? Could this lead to both parties paying the other larger and larger sums forever? It is a fun thing to think about at least.

Yes, this is AIMD and it's well formalised and understood.

For those reading this far into the thread, here is a reference to AIMD [1]. Reading through, there is cross-over in the idea but I don't think it 100% covers things. A good starting point to look at though.

[1] https://www.geeksforgeeks.org/computer-networks/aimd-algorit...

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