Rent seeking with efforts and bids

We introduce bids in a rent-seeking contest. Players compete for a prize. Apart from exerting lobbying efforts, they also submit a bid which is payable only if they win the prize. We show that our model has a unique Nash equilibrium in pure strategies, in which each active player submits the same bid, while the sum of all efforts equals that bid. In equilibrium there is underdissipation of rent.