The investment banker guarantees to the company that they will purchase all of the shares. But they intend to sell them, or at least the bulk of them, immediately to their institutional clients. Since the price is not determined until the last minute, institutions put in a subscription request for a certain number of shares, but the exact cost is unknown. They are not obligated to take any or all of the shares, if they so choose. Investment bankers gauge the demand, and set a price as high as they can, balanced by trying to ensure that everyone will buy it.
Institutions are no different than any one else.
Some will argue the price. Others will just place an order. Some will buy the IPO shares for long term holding. Others will flip them as soon as possible. The investment bankers, who will be market makers in the stock, prefer to have friendly hands holding the stock for as long as possible.