Rivalry as a plot or an element in the plot of a story can add a layer of tension. Two people vie for the same goal, And they must be two people of equal strength. For one to be weaker would lose the potential tension. Here you have the protagonist and the antagonist battling for a reward only one of them can win. This is a struggle for power. While they both have strengths they do not have to be the same strengths. These strengths can be in opposition and need to be compensating and matching.
Think of a battle of wills and start the story showing the pair in competition where one of them appears to win. Al least for the moment. As one seems to rise, the other will appear to fall. There are moral issues involved such as greed versus generosity.
Next work in a reversal where the man or woman on the bottom rises to the top and the other remains where they were at the end of the first confrontation. Once this is established the time has come for the final confrontation and the protagonist emerges with victory. Then he or she can restore order to their world.