Learning rivals' information in interdependent value auctions

We study a simple auction model with interdependent values in which there are two bidders each of whom observes a binary signal and can learn rival's information at a cost, whereafter they compete in the first-price or second-price auction. We characterize a unique symmetric equilibrium strategy—learning and bidding strategies—for the two auction formats. In the first-price auction, bidders with high signal learn rival's information with higher probability than those with low signal do. In the second-price auction, bidders never learn rival's information. The bidders' learning in the first-price auction causes an efficiency loss. Its impact on the seller's revenue depends on the parameter values. When the learning cost is low or values are sufficiently interdependent, the learning intensifies the bidding competition and thereby increases the revenue in the first-price auction, which means the learning entails an efficiency/revenue trade-off across the auctions formats. Otherwise, the first-price auction is dominated by the second-price auction in terms of both efficiency and revenue. Extensions of our model show the robustness of our results and intuition behind them.