Pricing combinatorial auctions

Single-item auctions have many desirable properties. Mechanisms exist to ensure optimality, incentive compatibility and market-clearing prices. When multiple items are offered through individual auctions, a bidder wanting a bundle of items faces an exposure problem if the bidder places a high value on a combination of goods but a low value on strict subsets of the desired collection. To remedy this, combinatorial auctions permit bids on bundles of goods. However, combinatorial auctions are hard to optimize and may not have incentive compatible mechanisms or market-clearing individual item prices. Several papers give approaches to provide incentive compatibility and imputed, individual prices. We find the relationships between these approaches and analyze their advantages and disadvantages.