You have no obligation to divulge to the first offer that a subsequent offer came in, or notify buyer 1 that it is now a multiple offer after 2nd offer came in. Often buyers pull out if it becomes a bidding war, so you don't want to lose the first full priced offer if it is the stronger of the two offers and leave you with one written offer on the table from a buyer then who has the power. Best bet is to negotiate with 2nd offer without announcing it to the first offer Unless the first offer has a home sale contingency I would not tell them about offer number 2. Don't focus on price so much, focus on terms! A cleaner deal at the same price is better than a higher offer with more hurdles or contingencies.
I like the idea of offering backup offer to keep the winning offer in line with home inspection issues.
Assuming you have an agent, and this isn't a dual agency situation with one of the offers, follow your agents counsul.
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