Why did Louis IV agree to share power with Frederick of Austria?

Louis IV agreed to share power with his prisoner, Frederick of Austria, primarily as a strategic maneuver to break up a hostile political alliance forming against him.1

By 1324, Louis faced increasing pressure from an alliance consisting of France, the Luxembourg dynasty, and the Austrians. By offering to share rule with Frederick, who had been his rival for the German crown, Louis successfully disrupted this coalition. Although the arrangement was initially complicated by the objections of Frederick’s brother, Duke Leopold, the eventual failure of the pope to support Frederick’s sole rule convinced Frederick that he had been manipulated by the Curia. Consequently, Frederick abandoned the hostile alliance and became a loyal co-ruler with Louis.12