Optimal seedings in interdependent contests

We study a model of two interdependent contests and heterogeneous players with commonly known types. The winners of both contests have winning values that depend on the types (abilities) of both winners. Therefore, endogenous win probabilities in each match depend on the outcomes of the other contests through the identity of the winner. The designer seeds players according to their types in order to maximize (minimize) the total effort. For such interdependent contests, each of which includes two heterogeneous players, we consider two different types of a winning value function and demonstrate that for multiplicative value functions it is optimal to place the two highest type players in different contests. On the other hand, for additive value functions it is optimal to place the two highest type players in the same contest since otherwise they practically do not affect each other.