Yeah every participant submit bid, the highest bidder is chosen. That is called bidding war.
No,
a bidding war is (requires an Open ascending-bid auction):
I bid 1$, you bid 2$, then I bid 3$, you bid $3.50 I bid $4, you $4.25, I bid $4.50, and you walk away and I win the auction on the item that is objectively worth $3.
First price bidding is:
I estimate the value at $3, I expect others to bid the same, I place a bid a $3.25
You estimate the value at $2.75, you expect others to bid the same, you place a bid a $3.00.
I win the auction at at $3.25
Second price bidding is:
I estimate the value at $3, but I'm willing to spend more because I really want the item, so I can pay up to $5 so I bid $5
You estimate the value at $2.75, but you have a tight budget and can live with out the item, you place a bid at $3.25.
I win the auction at $3.26
A bidding war can only ever occur in open auction because the other auction type don't allow the buyers to make subsequent bids.