Signaling in a Rent-Seeking Contest with One-Sided Asymmetric Information

We consider a two-player rent-seeking Tullock contest where one player has private information about his valuation of the prize, which can be high or low. This player can send a costly signal to his opponent, i.e., he can commit to reduce the prize either by some absolute amount of money or proportionally, conditional on winning it. We show that both kinds of signaling imply completely opposite results for separating equilibria, both in terms of conditions for existence and the type of player who sends the costly signal.