A way to make simple checks a little more detailed and flavorful.

You say a number and everyone involved keep saying higher numbers or passing. You can jump up as high as you want.

Once the auction is over, the highest bidder needs to beat that DC. If they fail, the second highest bidder gets a chance etc, but the lowest bidder autosucceeds.

You need to say what you do in order to get to say a number.

More than two people can be involved but in this example let's say it's Bob the thief trying to pick a lock.

Bob has +5 on his thieves' tools proficiency, and let's say this is a +4 lock.

Bob: "I put my tension tool in the main lock body and and start feeling around with my pick. Four."
DM: "The first couple of pins are loose, it's hard to find a bind. Eight."
Bob: "I apply harder tension and start from the back pins. 12."
DM: "The back pin is binding. It feels little weird. Could be a security pin. 15."
Bob: "I try to put that pin into place at least enough so I can get find a new binding pin. 16."
DM: "The next pin seems also to fall into place pretty easily. Go ahead and roll vs DC 16."
Bob: "I'm gonna spend insp to get advantage. Wow, I made it! Barely! 17!
DM: "The lock clicks open. What do you do?"

If Bob had stopped the bidding after the DM said 15, the DM would have to roll the lock's +4 value vs 15 in order to stay locked! Otherwise Bob would've gotten in that way.

(For DM: To get the mod, take the DC times two and then subtract 25. So DC 15 = +5. Or if it's an opposed check just use the NPC's skill as per any opposed check.)

It's difficult to do the following step online.

Before the bidding, the people involved roll a secret d6 and looks at it. (Or draw a playing card or initiative card, w/e.) This value something they will add to their roll in addition to adding their normal check bonus, so bid a little higher to compensate. It's there to add a little bit more of bluffing and tension to the auction.

Without this "secret" rule it's pretty easy to figure out an optimal number to bid. So if we can come up with a way to do "the secret" online that'd be best.