A tool for off-line experimentation with auction parameters for auctions for an ad space. The tool computes, using historical bid information, values per click to advertisers competing for the ad space. The tool applies a homotopy algorithm, using these values, to predict equilibrium bids based on the values to the advertisers. In computing the equilibrium bids, the bid of each advertiser is assumed to stay fixed over multiple auction cycles, but each advertiser is assumed to face uncertainty about quality scores used by the advertising platform in selecting bids and the rank of their bid with respect to others. The quality scores also are assumed to vary between auctions.