8. Combinatorial Auction Models

A similar rule was applied in the French auction of radio spectrum in 2011.

Parkers [63] studies the characteristics of the main models of ICAs. In this chapter, we will only focus on a subset of these models.

The simultaneous ascending auction (SAA) that we analyze in Chap. 5 could be considered to be an ICA if package bidding throughout the different rounds were allowed.

For more information regarding this auction model, see [9].

The preferences communicated by bidder i to his proxy bidder for each item, \(v_{i}^{\mathrm{proxy}}(S)\), do not necessarily have to coincide with their true values, v _i (S).

For the specific case of a single item, this model is similar to auctions conducted on the Internet, in which the bidder indicates the maximum bid that he is willing to submit, and the system automatically updates the bids as long as the maximum bid is higher than the actual bid, and the bidder is not the provisional winner.

Items within the same category are homogeneous items and heterogeneous among categories.

Throughout the entire clock phase and in the transition to the proxy phase, the seller may establish an activity rule to encourage the bidders to bid according to their true preferences from the beginning of the auction. One option is to select an activity rule that presents monotonicity in quantity, which implies that as the price increases, the demanded quantity cannot increase. A weaker activity rule is monotonicity of aggregate quantity across a group of items, such that the aggregate quantity demanded cannot increase as the price increases, which allows shifting quantities among products (this is the eligibility-based activity rule described in Chap. 5). However, the activity rule proposed by the inventors of this model is the revealed-preference activity rule because it gives more flexibility to the bidders when there are substitutes and complements items. For more details regarding this rule, see the appendix at the end of this chapter or [8].

The proxy phase with mandatory proxy bidding (bidders not allowed to change their reported preferences) is observationally equivalent to a sealed-bid auction, see [8].

Mochon et al. [55] analyzed the possible outcomes obtained when using this auction model to allocate radio spectrum licenses by means of genetic algorithms.

Different governments have used this auction mechanism to award spectrum licenses: Switzerland (2012), United Kingdom (2012), or Canada (2013).

The seller can set a limit on the maximum amount of the supplementary bids of each bidder based on his clock rounds bidding. Thus bidders have incentives to bid according to their true values throughout the auction.

We assume that according to the activity rule, the eligibility of round t equals the activity of round t − 1.