struggle for superiority

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In that memorable struggle for superiority between the rival houses of AUSTRIA and BOURBON, which so long kept Europe in a flame, it is well known that the antipathies of the English against the French, seconding the ambition, or rather the avarice, of a favorite leader,[10] protracted the war beyond the limits marked out by sound policy, and for a considerable time in opposition to the views of the court.
So it's not a struggle for superiority or special treatment, but balance.
In this brave new world the major corporate players are GlobeNet and WilCon locked in a relentless struggle for superiority.
After a long struggle for superiority, Huntly went further ahead in the second half through a Stewart tap-in from a Marco de Barros cutback.