We study vote splitting in elections. Vote splitting refers to the phenomenon that the participation of candidates with little chances of winning has the effect of splitting votes away from more popular candidates. We develop a model of an electoral game with two parties, each consisting of one strong candidate and some weak candidates. We analyze strong candidates' incentives to give side transfers to weak candidates to manipulate their campaign participation decisions. We then derive the winning probabilities of the strong candidates in equilibrium. We show that under some conditions, the side transfers that one weak candidate receives are independent of the campaign cost and bias of the other weak candidate. We also study the role of uncertain campaign costs of weak candidates. In particular, we show that if the campaign cost of one party's weak candidate is uncertain when strong candidates decide side transfers, then the strong candidate from the other party will be more likely to win than the case with full information.
