A pure variation of risk in first-price auctions

We introduce a new method of varying the risk that bidders face in first-price private value auctions. We find that decreasing bidders' risk significantly reduces the degree of overbidding relative to the risk-neutral Bayesian-Nash equilibrium prediction. This implies that risk affects bidding behavior as generally expected in auction theory. While resolving a long-standing debate on the effect of risk on auction behavior, our results give rise to a new puzzle. As risk is diminished and overbidding decreases for most of the value range, a significant degree of underbidding sets in for very low values.