At an auction, I bid on an item. 16 more bidders want that item, all of whom place upward pressure on the price. We all have our ceiling - the price we won't go above, and the auction tends to test these ceilings as a) two or more people who value an item CAN, DO and WILL compete against each other to acquire the same item, AND b) even as each individual really does set their personal CEILING price to their personal value of that item. But it's not just that one item, nor is it all about a single buyer's willingness to pay more. Buyers are MORE WILLING to pay less, and will WORK to pay less.
Part of the ceiling price for each buyer is lowered by the knowledge that OTHER sellers are around with the same item. Or a substitute item. And buyers will WORK to seek out these alternate sellers - because they are also competing. When there are two or more sellers of the same item, they tend also to a) compete with each other for buyers, and can also b) set their FLOOR price, below which they are unwilling to sell.
Buyers compete with buyers, just as sellers compete with sellers, but once interest in an item is established, there is essentially no difference between buyers and sellers. They are just TRADERS of unlike items. Nothing more, really.