There is a couple of reasons I can think of as to why someone would run up the bidding. If the buyers both regularly buy the same thing, ( collectables maybe ) , one buyer could make sure the other pays top price to reduce their spending power on future auctions. I used to attend physical auctions regularly and this used to happen on occasions.
If both buyers are dealers and planning to re-sell the items, they may be trying to dent the others profit margins by making them pay top dollar. Many dealers work on an averaging system, bidding higher than they expect to pay on the principle that some items will be cheaper, some dearer, but the overall prices will average out OK. By averaging their sales they keep the opposition away from choice items, meaning the unsuccesfull bidder has wasted their time and energy with little to show for it. . If another buyer runs them up to full price on all items it blows the averaging strategy out of the water and leaves the "succesfull" buyer with a large bill and small profit.
Both of these stratagies are quite common at physical real life auctions.
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