This discussion paper led to an article in <I>Games and Economic Behavior</I> (2011). Vol. 72, pp. 594-601.<P> There is by now a large literature arguing that auctions with a variety of after-market interactions may not yield an efficient allocation of the objects for sale, especially when the bidders...</p></i>

People overestimate the probability that others share their values or preferences. I introduce type projection equilibrium (TPE) to capture such projection in Bayesian games. TPE allows each player to believe his opponents share his type with intermediate probability \rho. After establishing...

The theoretical literature on collusion in auctions suggests that the first-price mechanism can deter the formation of bidding rings. In equilibrium, collusive negotiations are either successful or are avoided altogether, hence such analysis neglects the effects of failed collusion attempts. In...

We study first- and second-price private value auctions with sequential bidding where second movers may discover the first movers bids. There is a unique equilibrium in the first-price auction and multiple equilibria in the second-price auction. Consequently, comparative statics across price...

In many auction settings, there is favoritism: the seller's welfare depends positively on the utility of a subset of potential bidders. However, laws or regulations may not allow the seller to discriminate among bidders. We find the optimal nondiscriminatory auction in a private value,...

We study first- and second-price private value auctions with sequential bidding where second movers may discover the first movers bids. There is a unique equilibrium in the first-price auction and multiple equilibria in the second-price auction. Consequently, comparative statics across price...

This paper solves the equilibrium bid functions of third- and higher-price auctions for a large class of distribution functions of bidders' valuations, assuming the symmetric independent private values framework, and risk neutrality. In all these auctions, equilibrium bids exceed bidders'...