Here’s a strategy that we used back in 2000 when there were multiple offers on a house we ended up buying (and eventually sold in 2005).
Use an escalator clause.
Offer some initial amount, with an escalator of $1000 above any higher offer up to some limit, with the clause that they must produce proof of the higher offer in writing. Make sure the higher limit is the most you would pay.
When we did this our offer at the initial amount was accepted.
Either the “other buyer” flaked or the agent was bluffing, or the other offer was lower in the first place.
FWIW, at that time we bought the initial price we set was about $270K, and our escalator went in 500 increments to 280K, which we were willing to pay.
