There are many types of auctions.
In an auction an agent playing the role of auctioneer sells an item on behalf of an agent playing the role of seller. Agents playing the bidder role bid on the item.
There are several optional roles. An agent playing the role of doorman registers bidders for an auction. An agent playing the role of accountant holds the item in escrow until the money is paid.
Note: only one item is sold in an auction. If there are multiple items to be sold, then there must be multiple auctions.
Examples: art, antiques, flowers, and tobacco are commonly sold at auctions.
Example: web sites like eBay offer online auctions.
An auction begins when a seller offers an item to be sold. The seller specifies a minimum price that he will accept for the item. This becomes the current bid.
In an English auction (also called an ascending price auction), the auctioneer broadcasts the current bid, then waits for new bids for a specified time period. If no bids are received during this time period, then the item is sold to the bidder who offered the current bid. Otherwise, the highest bid is selected from new batch of bids and the process repeats itself. If there is a tie for the best bid, then the first bidder is selected.
Sequence and activity diagrams are left as an exercise to the reader.