Why do Presidential candidates participate in debates?

Some of them want to debate because they think the debate will help them get elected. They are confident in their debating skills and welcome the chance to be seem and by millions on national TV.

Others are not so confident, but are afraid they will look cowardly and lose votes if they refuse to debate, so they make the most of the situation and try to draw up rules that will favor them or at least level the playing field.