2,457 research outputs found
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.
Modelling Combinatorial Auctions in Linear Logic
We show that linear logic can serve as an expressive framework
in which to model a rich variety of combinatorial auction
mechanisms. Due to its resource-sensitive nature, linear
logic can easily represent bids in combinatorial auctions in
which goods may be sold in multiple units, and we show
how it naturally generalises several bidding languages familiar
from the literature. Moreover, the winner determination
problem, i.e., the problem of computing an allocation of
goods to bidders producing a certain amount of revenue for
the auctioneer, can be modelled as the problem of finding a
proof for a particular linear logic sequent
Iterative Combinatorial Auctions: Theory and Practice
Combinatorial auctions, which allow agents to bid directly for bundles of resources, are necessary for optimal auction-based solutions to resource allocation problems with agents that have non-additive values for resources, such as distributed scheduling and task assignment problems. We introduce iBundle, the first iterative combinatorial auction that is optimal for a reasonable agent bidding strategy, in this case myopic best-response bidding. Its optimality is proved with a novel connection to primal-dual optimization theory. We demonstrate orders of magnitude performance improvements over the only other known optimal combinatorial auction, the Generalized Vickrey Auction.Engineering and Applied Science
Multiagent resource allocation with k-additive utility functions
We briefly review previous work on the welfare engineering framework where autonomous software agents negotiate on the allocation of a number of discrete resources, and point out connections to combinatorial optimisation problems, including combinatorial auctions, that shed light on the computational complexity of the framework. We give particular consideration to scenarios where the preferences of agents are modelled in terms of k-additive utility functions, i.e. scenarios where synergies between different resources are restricted to bundles of at most k items. Key words: negotiation, representation of utility functions, social welfare, combinatorial optimisation, bidding languages for combinatorial auctions
An Agent Based Market Design Methodology for Combinatorial Auctions
Auction mechanisms have attracted a great deal of interest and have been used in diverse e-marketplaces. In particular, combinatorial auctions have the potential to play an important role in electronic transactions. Therefore, diverse combinatorial auction market types have been proposed to satisfy market needs. These combinatorial auction types have diverse market characteristics, which require an effective market design approach. This study proposes a comprehensive and systematic market design methodology for combinatorial auctions based on three phases: market architecture design, auction rule design, and winner determination design. A market architecture design is for designing market architecture types by Backward Chain Reasoning. Auction rules design is to design transaction rules for auctions. The specific auction process type is identified by the Backward Chain Reasoning process. Winner determination design is about determining the decision model for selecting optimal bids and auctioneers. Optimization models are identified by Forward Chain Reasoning. Also, we propose an agent based combinatorial auction market design system using Backward and Forward Chain Reasoning. Then we illustrate a design process for the general n-bilateral combinatorial auction market. This study serves as a guideline for practical implementation of combinatorial auction markets design.Combinatorial Auction, Market Design Methodology, Market Architecture Design, Auction Rule Design, Winner Determination Design, Agent-Based System
Rate of Price Discovery in Iterative Combinatorial Auctions
We study a class of iterative combinatorial auctions which can be viewed as
subgradient descent methods for the problem of pricing bundles to balance
supply and demand. We provide concrete convergence rates for auctions in this
class, bounding the number of auction rounds needed to reach clearing prices.
Our analysis allows for a variety of pricing schemes, including item, bundle,
and polynomial pricing, and the respective convergence rates confirm that more
expressive pricing schemes come at the cost of slower convergence. We consider
two models of bidder behavior. In the first model, bidders behave
stochastically according to a random utility model, which includes standard
best-response bidding as a special case. In the second model, bidders behave
arbitrarily (even adversarially), and meaningful convergence relies on properly
designed activity rules
On the Economic Efficiency of the Combinatorial Clock Auction
Since the 1990s spectrum auctions have been implemented world-wide. This has
provided for a practical examination of an assortment of auction mechanisms
and, amongst these, two simultaneous ascending price auctions have proved to be
extremely successful. These are the simultaneous multiround ascending auction
(SMRA) and the combinatorial clock auction (CCA). It has long been known that,
for certain classes of valuation functions, the SMRA provides good theoretical
guarantees on social welfare. However, no such guarantees were known for the
CCA.
In this paper, we show that CCA does provide strong guarantees on social
welfare provided the price increment and stopping rule are well-chosen. This is
very surprising in that the choice of price increment has been used primarily
to adjust auction duration and the stopping rule has attracted little
attention. The main result is a polylogarithmic approximation guarantee for
social welfare when the maximum number of items demanded by a
bidder is fixed. Specifically, we show that either the revenue of the CCA is at
least an -fraction of
the optimal welfare or the welfare of the CCA is at least an
-fraction of the optimal welfare, where
is the number of bidders and is the number of items. As a corollary, the
welfare ratio -- the worst case ratio between the social welfare of the optimum
allocation and the social welfare of the CCA allocation -- is at most
. We emphasize that this latter
result requires no assumption on bidders valuation functions. Finally, we prove
that such a dependence on is necessary. In particular, we show
that the welfare ratio of the CCA is at least
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