Greedy Approach vs. GVA Optimal Scheme: Simulation on the Competitive Ratio and Revenues

Combinatorial auction is an auction such that multiple goods are available and bidders can post bids for subsets of the goods. An auction mechanism is composed of a goods allocation rule and a payment scheme, which balance the goal of maximizing the sellers’ revenue and encouraging truthful declaration of bidders. The original Generalized Vickrey Auction (GVA) allocates the goods by maximizing the declared value of allocations and adopts a generalized second price payment scheme (Clarke’s scheme) to enforce truthfulness. However, the implementation of GVA is NP-hard even under the assumption of Single Minded Bidders (SMB). To solve the problem, a greedy allocation mechanism is proposed to achieve polynomial time in the number of goods k. The best greedy allocation can reach the competitive ratio of √ k to the optimal GVA allocation. However, Clarke’s payment scheme no longer guarantees the truthfulness for greedy allocations. In exploring the truthfulness design, Lehmann et al [3] proposed a sufficient condition for truthful mechanisms and a truthful greedy payment scheme.