Basic auction theory revisited

Abstract

We revisit the benchmark model of auctions and consider a more general class of utility functions that allow for income effects. We assume that all individuals have the same utility function but have different incomes. Incomes are private information. We analyze first‐price, second‐price, and all‐pay auctions and show that non‐quasilinearity changes many basic results of the benchmark model. While Vickrey's () result on second‐price auctions is very robust, revenue equivalence breaks down even with risk‐neutral bidders, high enough incomes and identically and independently distributed types. In most cases, we find that all‐pay auctions fetch the highest expected revenue.