Full surplus extraction by a risk averse seller in correlated environments

We study an auction setting with risk averse seller and correlated bidders' values. We first rely on a result by Che and Kim [Che, Y.-K., Kim, J., 2005. Robustly Collusion-Proof Implementation. Mimeo, University of Wisconsin, available at http://www.ssc.wisc.edu/~yche/home.htm.] to argue that when there are enough bidders and/or types, the seller can generically obtain both the complete information expected revenue and perfect insurance. Then we consider a specific two-bidder-two-type environment in which the above first-best is not attainable and examine the seller's incentives to leave rents to the bidders and/or to allocate the object inefficiently in order to reduce his risk. We find that: (i) no tradeoff exists between risk and extracting the bidders' rents when correlation is negative and strong; (ii) the seller's expected revenue is lower than under complete information if he is sufficiently risk averse and/or correlation is weak; and (iii) allocative efficiency may decrease as correlation becomes stronger.