How to Not Let Them Get Away with It: The Mathematics of Infinite Exploitation

3 hours ago

The author reflects on a personal experience during home buying where sellers demanded half the savings from providing their title insurance policy, described as exploitative.
A theoretical counter-response uses a sequential bargaining game (ultimatum game) to propose infinite rounds of splitting unexpected savings, leveraging geometric series.
In the infinite bargaining model with equal splits each round, buyers end up with 2/3 of the savings and sellers with 1/3, derived from a geometric series sum.
Generalizing to any initial seller cut c, buyers ensure at least half of the total savings M, with sellers receiving M*c/(1+c) after infinite rounds.
Extending to infinite rounds of infinite negotiations, sellers' share approaches zero, illustrating a strategic defeat via function iteration f(x)=x/(1+x).
In reality, the buyers rejected the offer and obtained the policy elsewhere, securing savings without conceding to the sellers' terms.

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