Rationalizable bidding in first-price auctions

We analyze the consequences of strategically sophisticated bidding without assuming equilibrium behavior. In particular, we characterize interim rationalizable bids in symmetric first-price auctions with interdependent values and affiliated signals. We show that (1) every nonzero bid below the equilibrium is rationalizable, (2) some bids above the equilibrium are rationalizable, (3) the upper bound on rationalizable bids of a given player is a nondecreasing function of her signal. In the special case of independent signals and quasi-linear valuation functions, (i) the least upper bound on rationalizable bids is concave; hence (ii) rationalizability implies substantial proportional shading for high valuations, but is consistent with negligible proportional shading for low valuations. We argue that our theoretical analysis may shed some light on experimental findings about deviations from the risk-neutral Nash equilibrium.