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Optimal Auction Design for Agents with Hard Valuation Problems
As traditional commerce moves on-line more business transactions will be mediated by software agents, and the ability of agent-mediated electronic marketplaces to efficiently allocate resources will be highly dependent on the complexity of the decision problems that agents face; determined in part by the structure of the marketplace, resource characteristics, and the nature of agentsâ local problems. We compare auction performance for agents that have hard local problems, and uncertain values for goods. Perhaps an agent must solve a hard optimization problem to value a good, or interact with a busy and expensive human expert. Although auction design cannot simplify the valuation problem itself, we show that good auction design can simplify meta-deliberation - providing incentives for the ârightâ agents to deliberate for the ârightâ amount of time. Empirical results for a particular cost-benefit model of deliberation show that an ascending-price auction will often support higher revenue and efficiency than other auction designs. The price provides agents with useful information about the value that other agents hold for the good.Engineering and Applied Science
Truthful approximation mechanisms for restricted combinatorial auctions
When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness).
We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann, O'Callaghan, and Shoham, who presented greedy heuristics. We show how to use If-Then-Else constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios
Public projects, Boolean functions and the borders of Border's theorem
Border's theorem gives an intuitive linear characterization of the feasible
interim allocation rules of a Bayesian single-item environment, and it has
several applications in economic and algorithmic mechanism design. All known
generalizations of Border's theorem either restrict attention to relatively
simple settings, or resort to approximation. This paper identifies a
complexity-theoretic barrier that indicates, assuming standard complexity class
separations, that Border's theorem cannot be extended significantly beyond the
state-of-the-art. We also identify a surprisingly tight connection between
Myerson's optimal auction theory, when applied to public project settings, and
some fundamental results in the analysis of Boolean functions.Comment: Accepted to ACM EC 201
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
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