Auctions with rent seeking

We present a model which combines elements of an auction and a rent-seeking contest. Players compete for a prize. Apart from exerting lobbying efforts, they also have to submit a bid which is payable only if they win the prize. First, we analyze the model if the returns-to-scale parameters of both bids and efforts are unity. We present a necessary and sufficient condition for the existence of a unique Nash equilibrium. In the equilibrium each player submits the same bid, while the sum of all efforts equals that bid. Second, we analyze the case in which the returns-to-scale parameters may differ from unity, and derive the implications of that specification.