MAX-Functionとサブセレクトを使用して、各オークションの最高入札額を取得できます。この副選択を他のテーブルと結合し、where句を次のように設定すると、探しているものが得られるはずです。
SELECT a.id, a.title, ab.bid_points, u.display_name
FROM Auction AS a
INNER JOIN (SELECT auction_id, MAX(bid_points) AS maxAmount FROM auction_bids GROUP BY auction_id) AS maxBids ON maxBids.auction_id = a.id
INNER JOIN auction_bids AS ab ON a.id = ab.auction_id
INNER JOIN users AS u ON u.id = ab.user_id
WHERE ab.auction_id = maxBids.auction_id AND ab.bid_amount = maxBids.maxAmount
お役に立てば幸いです。