Depending on whom you ask, U.S. President Donald Trump’s Executive Order pausing enforcement of the Foreign Corrupt Practices Act is either the end of anti-corruption as we know it, or the beginning of a needed discussion about how the law is enforced. But lost in the hand-wringing and pish-poshing is perhaps the most important question for businesses: How will America’s competitors react?

Corruption is notoriously difficult to detect. As I describe in the book that I recently published...