What a great idea - the Bible for a book review!
Well, the Pope would probably agree with your speaker. The Catholics would have loved the communists if they hadn't been Godless. The Catholics strongly believe in cooperation for the greater good, and in "from each according to his ability, to each according to his needs," one of the communist manifestos. Unfortunately the Godless aspect proved an insurmountable obstacle to cooperation with the communists, so Catholocism backs socialism instead.
Perhaps your speaker was using a particular definition of competition. If his definition excluded conflict (eg, murder, battles, wars), then perhaps he has a point, though I think two competitions can't possibly be right, because like you I can think of three off the top of my head. Another possibility is that he was focusing only on the NT.
The Bible is a big book and can be interpreted in many ways, with the expected result that there are many, many Christian religions. It is the Biblical interpretations of one particular portion of Christian religions usually known as evangelicals that is relevant to the debate here.
--Percy
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