Approximation in mechanism design with interdependent values

This paper studies the revenue maximization problem in environments wherein buyers have interdependent values and correlated types. We show that (1) when the system of feasible sets is a matroid and buyer valuations satisfy a single-crossing condition, the generalized Vickrey-Clarke-Groves mechanisms with lazy reserves (VCG-L) are ex-post incentive compatible and ex-post individually rational; (2) if, in addition, the valuation distribution satisfies a generalized monotone hazard rate condition, the VCG-L mechanism with conditional monopoly reserves is approximately optimal. Then we construct an ascending auction that implements the truth-telling equilibrium of a VCG-L mechanism in ex-post equilibrium. Finally, we discuss the connection between the VCG-L mechanisms and greedy algorithms studied in Lehmann et al. (2002) and deferred-acceptance auctions studied in Milgrom and Segal (2014), and the impact of competition by proving a Bulow and Klemperer (1996) type result.