Can Risk Aversion Mitigate Inefficiencies in Core-Selecting Combinatorial Auctions?

Core-selecting combinatorial auctions are being used in an increasing number of spectrum sales worldwide. It was shown that equilibrium strategies can lead to outcomes that are further from the core than the Vickrey outcome in sealed-bid auctions. Ascending core-selecting auctions can even lead to inefficient non-bidding equilibria. Risk aversion is arguably a significant driver of bidding behavior in high-stakes auctions. We analyze the impact of risk aversion on equilibrium bidding strategies and efficiency of core-selecting auctions in a threshold problem with one global and several local bidders. First, we characterize the necessary and sufficient conditions for the perfect Bayesian equilibria of the ascending core-selecting auction mechanism to have the small bidders to drop at the reserve price. In spite of the free-riding opportunities of local bidders, risk-aversion reduces the scope of the non-bidding equilibrium. Second, we derive equilibrium bidding strategies and revenue for sealed-bid core selecting auctions. Third, we show that in spite of the non-bidding equilibrium in the ascending auction, setting optimal reserve prices in each format leads to higher efficiency and revenue in the ascending than in the sealed-bid auction