How do brokers negotiate the purchase price?

then in many cases it can make sense to let the contract expire and then save many thousands of euros in broker fees.

Every craftsman who does NOT build with you is a happy craftsman. Every seller who sells NOTHING to you is a happy seller. You would try to cheat everyone, wouldn’t you?
Sometimes a service also costs money. Who pays, for example, the top listing on ImmoScout for 1,000€? You or the broker?

How long does such a broker contract run? If you let it run for 3 months now and extend it if necessary, then in many cases it can make sense to let the contract expire and then save many thousands of euros in broker fees.

You also have to be very careful there.. Because broker contracts also state that if after the contract expires a buyer purchases the house who got in contact with the seller through the broker, the commission must be paid to the broker!

So if you want to save broker fees, then look for a property that does not involve a broker!

There are also brokers with whom the contract can be properly terminated within the term. That shows confidence.

We had the following reasons for initially not hiring a real estate agent to sell our house/land:

- Costs (regardless of whether we or the buyer would have to pay them)
- bad experiences in earlier times
- the agent would be a third party involved in the sales process for us, with whom we would first have to negotiate and whose contract we would have to have legally reviewed before signing
- it is not clearly binding for us what the agent is liable for and in what context; in the usual advertising portals they (somewhat exaggeratedly) "always exclude any liability for almost everything"; as the property seller, it creates a high degree of uncertainty for me if I do not know what the agent tells which interested parties and then we might still be held accountable months/years later for something the agent, perhaps actually or allegedly based on our information, told the buyer
- we would almost have to do all the work ourselves anyway (taking nice photos, obtaining land register extracts and other documents, drawing floor plans, tidying up the house and garden, analyzing the advantages of the house, answering questions from interested parties (via the agent?), cleaning the house before visits by interested parties, ...); showing the house and garden is the least work

One argument which, from my point of view, speaks in favor of involving an agent, if it applies:
He might be better than we are at seriously identifying interested and solvent buyers. My husband and I simply showed the house to everyone. However, this was not that unpleasant, since we did not want to disadvantage anyone anyway and also had no notably bad experiences.

- we would have to do almost all the work ourselves anyway (arranging nice photos, obtaining land registry excerpts and other documents, drawing floor plans, getting the house and garden in shape, analyzing the advantages of the house, answering the questions of interested parties (via the real estate agent?)

I am of the opinion that a good real estate agent would indeed provide that service and take it off your hands. A not-so-good one less and less, down to the bad agent who does nothing except placing an ad on Ebay Classifieds and organizing a mass viewing appointment (open house) with you... Therefore, yes, it is important to check in advance what the agent does. Or you tell them they are welcome to search, but not exclusively.

Addendum: According to unanimous opinion, there seem to be people who simply look at houses for sale just for fun. Although I would never come up with such an idea and have other hobbies, if this group of people actually exists, a real estate agent might perhaps recognize this even before the viewing and we would not.