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

Market Experience and willingness to trade: evidence from repeated markets with symmetric and asymmetric information

Many studies have found a gap between willingness-to-pay and willingness-to-accept that is inconsistent with standard theory. There is also evidence that the gap is eroded by experience gained in the laboratory and naturally occurring markets. This paper argues that the gap and the effects of experience are explained by a caution heuristic. This conjecture is tested in a repeated market experiment with symmetric and asymmetric information. The results support the conjecture: people do seem to use heuristics rather than reacting optimally and their behavior adjusts slowly when the environment changes.WTA/WTP disparity, endowment effect, market experience, bounded rationality, asymmetric information

An Introduction to Mechanized Reasoning

Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics journals. We introduce mechanized reasoning to economists in three ways. First, we introduce mechanized reasoning in general, describing both the techniques and their successful applications. Second, we explain how mechanized reasoning has been applied to economic problems, concentrating on the two domains that have attracted the most attention: social choice theory and auction theory. Finally, we present a detailed example of mechanized reasoning in practice by means of a proof of Vickrey's familiar theorem on second-price auctions

Learning scalable and transferable multi-robot/machine sequential assignment planning via graph embedding

Can the success of reinforcement learning methods for simple combinatorial optimization problems be extended to multi-robot sequential assignment planning? In addition to the challenge of achieving near-optimal performance in large problems, transferability to an unseen number of robots and tasks is another key challenge for real-world applications. In this paper, we suggest a method that achieves the first success in both challenges for robot/machine scheduling problems. Our method comprises of three components. First, we show a robot scheduling problem can be expressed as a random probabilistic graphical model (PGM). We develop a mean-field inference method for random PGM and use it for Q-function inference. Second, we show that transferability can be achieved by carefully designing two-step sequential encoding of problem state. Third, we resolve the computational scalability issue of fitted Q-iteration by suggesting a heuristic auction-based Q-iteration fitting method enabled by transferability we achieved. We apply our method to discrete-time, discrete space problems (Multi-Robot Reward Collection (MRRC)) and scalably achieve 97% optimality with transferability. This optimality is maintained under stochastic contexts. By extending our method to continuous time, continuous space formulation, we claim to be the first learning-based method with scalable performance among multi-machine scheduling problems; our method scalability achieves comparable performance to popular metaheuristics in Identical parallel machine scheduling (IPMS) problems

A heuristic approach for the allocation of resources in large-scale computing infrastructures

An increasing number of enterprise applications are intensive in their consumption of IT, but are infrequently used. Consequently, organizations either host an oversized IT infrastructure or they are incapable of realizing the benefits of new applications. A solution to the challenge is provided by the large-scale computing infrastructures of Clouds and Grids which allow resources to be shared. A major challenge is the development of mechanisms that allow efficient sharing of IT resources. Market mechanisms are promising, but there is a lack of research in scalable market mechanisms. We extend the Multi-Attribute Combinatorial Exchange mechanism with greedy heuristics to address the scalability challenge. The evaluation shows a trade-off between efficiency and scalability. There is no statistical evidence for an influence on the incentive properties of the market mechanism. This is an encouraging result as theory predicts heuristics to ruin the mechanism’s incentive properties. Copyright © 2015 John Wiley & Sons, Ltd