A new bidding framework for combinatorial e-auctions

Bidding languages define the means through which participants in an electronic auction define bids and express requirements on their execution. The current state of combinatorial auction market design indicates that no existing bidding language is general enough to support auctions of both divisible and indivisible commodities. In this paper, we propose a novel bidding framework based on a two-level representation of a combined bid. At the inner level, bidding operators impose conditions on the executed proportions of packages of atomic single-item bids. Partial bids defined in this way are then recursively combined through logical operators to produce a final combined bid that is submitted to the auctioneer. We present a formal specification of the framework, and analyze how it impacts the mathematical programming formulation of the allocation problem. An application in the context of combinatorial auctions of financial assets illustrates the utilization of the proposed bidding framework.