Aggression of the Weak

This paper compares equilibrium bidding strategies in a first-price sealed-bid auction with two asymmetric bidders who have dependent private valuations. Modeling bidder strength via a stochastic asymmetry condition – where one bidder is systematically more likely to hold the maximum valuation – I show that the globally weak bidder, facing a competitive disadvantage at all top valuation levels, bids more aggressively at every valuation. Conversely, the stronger bidder wins more frequently, generalizing Maskin and Riley (2000) to dependent private-value environments. When the stochastic asymmetry flips once, so that each bidder is stronger over a different range, the bid distributions cross once, with each bidder bidding more aggressively where their competitive disadvantage is most acute. In both environments, allocative inefficiency is an inherent feature of the equilibrium, driven by the stronger bidder's heightened incentives to shade bids relative to their valuation. The results translate to procurement auctions and wage competition between employers, and extend to interdependent-value auctions and the war of attrition under modified conditions.