I dont know what branch of "game theory" this comes under but I figure that the banks first offer has to be their best offer.
This is similar to a redundancy situation where if there is an expectation of a better offer some time in the future than there will be little or no takers.
If I were a bank I would pitch it initially slightly higher then when a certain set amount had been achieved then shave off a few points until another threshold figure had been achieved. I would also publicise the fact that it was a limited time offer and that once the quota had been achieved that the next round would be on less favourable grounds.
This is similar to a redundancy situation where if there is an expectation of a better offer some time in the future than there will be little or no takers.
If I were a bank I would pitch it initially slightly higher then when a certain set amount had been achieved then shave off a few points until another threshold figure had been achieved. I would also publicise the fact that it was a limited time offer and that once the quota had been achieved that the next round would be on less favourable grounds.