I think the important difference to note here is between the two verbs 始まる and 始める:
Furthermore, note that the particle "を" often marks the direct object of a verb, and the particle "が" often marks the subject of a verb.
In your sentence, the 競り "has started" (始まりました), which means that 競り is the subject, therefore it uses が.
Hypothetically, if the sentence was phrased differently and "somebody" was starting the 競り, then you might use が to mark the "somebody", and を to mark the "something" (the 競り), and you would use the verb 始める instead of 始まる。