プレイヤーごとに最高のスコアを選択する

valueごとに 、グループごとの最大値 を取得できます。 ：

SELECT * FROM Scores NATURAL JOIN (
  SELECT player_id, value1, value2, MAX(value3) value3 FROM Scores NATURAL JOIN (
  SELECT player_id, value1, MAX(value2) value2         FROM Scores NATURAL JOIN (
  SELECT player_id, MAX(value1) value1                 FROM Scores
    GROUP BY player_id) t
    GROUP BY player_id) t
    GROUP BY player_id) t
ORDER BY value1 DESC, value2 DESC, value3 DESC

sqlfiddle でご覧ください 。