I've never faced this situation. Generally, I like to hold at what works for me and stretch only if it's worth it. Renegotiating because you never intended to pay your offer price - might work a few times, but seems like a losing strategy to your reputation.
How about offering better terms?
If you suspect the other guy's going to 'renegotiate', how about offering a 30 day due diligence period and then the earnest money goes hard. After that, no more renegotiations and you get another 30-45 days for financing to come through (financing contingency).
Then the seller can go to the other buyer and see if they'll match terms.
If the other buyer won't match terms because they want to stretch things out to strengthen their renegotiation position, then at least the seller will know that's a potential risk.
If the other buyer matches, at least in 30 days, the seller will know if the buyers is full of it or really going to close at the stated price and if the buyer wants to renegotiate, seller can go back to you and only have wasted 30 days.
Or you can offer more earnest money down. Then if the other buyer has to match, that puts him in a riskier position, because if he tries to renegotiate later and the seller says No (because he realizes that they've fooled him) then the buyer will have had more capital not being used productively.