Overbidding and underbidding in package allocation problems

We study the problem of allocating packages of different objects to a group of bidders. A rule is overbidding-proof if no bidder has incentives to bid above his actual valuations. We prove that if an efficient rule is overbidding-proof, then each winning bidder pays a price between his winning bid and what he would pay in a Vickrey auction for the same package. In counterpart, the set of rules that satisfy underbidding-proofness always charge a price below the corresponding Vickrey price. A new characterization of the Vickrey allocation rule is provided with a weak form of strategy-proofness. The Vickrey rule is the only rule that satisfies efficiency, individual rationality, overbidding-proofness and underbidding-proofness. Our results are also valid on the domains of monotonic valuations and of single-minded bidders. Finally, a rule is introduced that is overbidding proof and its payoffs are bidder-optimal in the core of the auction game according the reported valuations

Quadratic Core-Selecting Payment Rules for Combinatorial Auctions

We report on the use of a quadratic programming technique in recent and upcoming spectrum auctions in Europe. Specifically, we compute a unique point in the core that minimizes the sum of squared deviations from a reference point, for example, from the Vickrey-Clarke-Groves payments. Analyzing the Karush-Kuhn-Tucker conditions, we demonstrate that the resulting payments can be decomposed into a series of economically meaningful and equitable penalties. Furthermore, we discuss the benefits of this combinatorial auction, explore the use of alternative reserve pricing approaches in this context, and indicate the results of several hundred computational runs using CATS data.Auctions, spectrum auctions, market design, package auction, clock auction, combinatorial auction

Optimal Shill Bidding in the VCG Mechanism

This paper studies shill bidding in the VCG mechanism applied to combinatorial auctions. Shill bidding is a strategy whereby a single decision-maker enters the auction under the guise of multiple identities (Sakurai, Yokoo, and Matsubara 1999). I formulate the problem of optimal shill bidding for a bidder who knows the aggregate bid of her opponents. A key to the analysis is a subproblem--the cost minimization problem (CMP)--which searches for the cheapest way to win a given package using shills. An analysis of the CMP leads to several fundamental results about shill bidding: (i) I provide an exact characterization of the aggregate bids b such that some bidder would have an incentive to shill bid against b in terms of a new property, Submodularity at the Top; (ii) the problem of optimally sponsoring shills is equivalent to the winner determination problem (for single minded bidders)--the problem of finding an efficient allocation in a combinatorial auction; (iii) shill bidding can occur in equilibrium; and (iv) the problem of shill bidding has an inverse, namely the collusive problem that a coalition of bidders may have an incentive to merge (even after competition among coalition members has been suppressed). I show that only when valuations are additive can the incentives to shill and merge simultaneously disappear.VCG mechanism, combinatorial auctions, winner determination problem, collusion.

Retail Warehouse Loading Dock Coordination by Core-selecting Package Auctions

Congestions at loading docks can cause severe delays in logistics processes and cause increasing bottlenecks for truck routes. For warehouses, uncoordinated arrivals of trucks make appropriate staffing difficult and congestions can interfere with other processes at the facility. To mitigate congestions at loading docks, we propose package auctions to allocate time slots to trucks. \ \ The contribution of this research is the application of core-selecting package auctions to address the loading dock congestion problem. We propose a bidding language and a core-selecting package auction for this setting based on existing literature. Core-selecting payment rules can avoid drawbacks of the Vickrey–Clarke–Groves (VCG) mechanism with Clarke pivot rule, e.g., low perceived fairness of prices. \ \ We evaluate our proposal by means of simulation and assess (i) the potential for waiting time reduction compared to uncoordinated arrivals as well as sharing of historical waiting times, (ii) the empirical complexity of the computational problem for scenarios of varying complexity, and (iii) the relation of VCG and bidder-Pareto-optimal core payments. Our findings provide evidence that loading dock auctions can alleviate congestion substantially and that the core-pricing rule is well-suited to address the price fairness and low seller revenue problems in this setting

On Quadratic Core Projection Payment Rules for Combinatorial Auctions

Auctions of licenses for electromagnetic spectrum conducted by the Federal Communications Commission (FCC) often involve the simultaneous sale of hundreds of licenses for wireless bandwidth in different geographic regions and in different spectral bands. The auctions can involve hundreds of bid- ding rounds over several weeks. A nontrivial open problem is to design an auction format that allows bidder flexibility, maximizes social welfare, and withstands legal scrutiny. We consider a recently introduced promising auction format called core projection auctions. It is based on a projection of a Vickrey price vector onto the core. The auction consists of two processes: winner determination process and payment determination process. The auction aims to make it easy for bidders to determine their bids by giving them little strategic advantage by having their bids deviate from their true valuation of the spectrum. This thesis explores properties of such a core projection mechanism with an emphasis on numerically analyzing the marginal incentive for bidders to bid untruthfully. By implementing solvers and running simulations, we conjecture that in general, the payment for a winner increases no faster than the corresponding bidding price.Ope