Many games use the auction and bidding mechanic as a way distributing resources in the game. There are many types of auctions that can be employed:

Traditional or English Auction: This is what most people think about when they hear auction. An item is posted for sale in front of a group of potential buyers who make bids and counter-bids out loud until there are no further bids. Then the last bidder “wins” the auction and buys the item at the last bid. There are many variants of this style, but the core issue is that the buyers publicly compete with each other to purchase the item by making ever increasing bids.

Clipboard English Auction: Usually used with charity functions where people contribute various items which are then publicly displayed. Participants then make written bids on a sheet of paper in front of the item. People can increase the bid by writing their name down and making a higher offer. At the end of the auction the highest bid wins.

Sealed Bid Auction: In a sealed bid auction, the name says it all. Bidders make blind secret bids, usually by placing their offer in an envelope, and after a certain amount of time the envelopes are opened, and the winner is announced. Usually no other information is provided.

Dutch Auction: Bidding starts at a very high price, and then the price is reduced until someone accepts the offer. Dutch auctions usually involve multiple units of the same item being sold one at a time.

In most games resources are allocated by either a random factor (drawing a card) or by earning points in some way. Adding an auction might make things interesting particularly if the game involves each player having similar or identical goals. Or perhaps even totally different goals?