Exploring pricing rules in combinatorial sealed-bid auctions

The allocation of public goods such as the radio spectrum is a difficult task that the government must face. Currently, auctions are becoming an important tool to deal with this duty. In this context, the rules that the auctioneer establishes are particularly relevant, as the final outcome depends on them. When auctioning many related items, such as spectrum licenses, the bidders’ values for one item may depend on the number of items already obtained (complements and substitutes items). In such circumstances, combinatorial auctions are the most appropriate alternative for allocating lots. This paper analyzes the implications of selecting a particular pricing mechanism on the final result in a combinatorial sealed-bid auction. The following pricing rules are selected: the first-price mechanism, the Vickrey–Clarke–Groves (VCG) mechanism, and the bidder–Pareto–optimal (BPO) core mechanism, a core-selecting auction. To test these pricing rules, a simulator of the auction model has been developed. Then, to tackle the complex problem of simulating bidders’ behavior, a co-evolutionary system has been designed to identify improved strategies. The results revealed that the first-price mechanism yields inefficient outcomes and a notable reduction in the seller's revenues. Both the VCG and BPO mechanisms yield outcomes that are closer to the efficient allocation, and differences in revenues are affected by the presence of asymmetries.