Mechanism Design for Perturbation Stable Combinatorial Auctions

Motivated by recent research on combinatorial markets with endowed valuations by (Babaioff et al., EC 2018) and (Ezra et al., EC 2020), we introduce a notion of perturbation stability in Combinatorial Auctions (CAs) and study the extend to which stability helps in social welfare maximization and mechanism design. A CA is $\gamma\textit{-stable}$ if the optimal solution is resilient to inflation, by a factor of $\gamma \geq 1$, of any bidder's valuation for any single item. On the positive side, we show how to compute efficiently an optimal allocation for 2-stable subadditive valuations and that a Walrasian equilibrium exists for 2-stable submodular valuations. Moreover, we show that a Parallel 2nd Price Auction (P2A) followed by a demand query for each bidder is truthful for general subadditive valuations and results in the optimal allocation for 2-stable submodular valuations. To highlight the challenges behind optimization and mechanism design for stable CAs, we show that a Walrasian equilibrium may not exist for $\gamma$-stable XOS valuations for any $\gamma$, that a polynomial-time approximation scheme does not exist for $(2-\epsilon)$-stable submodular valuations, and that any DSIC mechanism that computes the optimal allocation for stable CAs and does not use demand queries must use exponentially many value queries. We conclude with analyzing the Price of Anarchy of P2A and Parallel 1st Price Auctions (P1A) for CAs with stable submodular and XOS valuations. Our results indicate that the quality of equilibria of simple non-truthful auctions improves only for $\gamma$-stable instances with $\gamma \geq 3$

An Investigation Report on Auction Mechanism Design

Auctions are markets with strict regulations governing the information available to traders in the market and the possible actions they can take. Since well designed auctions achieve desirable economic outcomes, they have been widely used in solving real-world optimization problems, and in structuring stock or futures exchanges. Auctions also provide a very valuable testing-ground for economic theory, and they play an important role in computer-based control systems. Auction mechanism design aims to manipulate the rules of an auction in order to achieve specific goals. Economists traditionally use mathematical methods, mainly game theory, to analyze auctions and design new auction forms. However, due to the high complexity of auctions, the mathematical models are typically simplified to obtain results, and this makes it difficult to apply results derived from such models to market environments in the real world. As a result, researchers are turning to empirical approaches. This report aims to survey the theoretical and empirical approaches to designing auction mechanisms and trading strategies with more weights on empirical ones, and build the foundation for further research in the field

Design and Evaluation of Procurement Combinatorial Auctions

The main advantage of a procurement combinatorial auction (CA) is that it allows suppliers to express cost synergies through package bids. However, bidders can also strategically take advantage of this flexibility, by discounting package bids and "inflating" bid prices for single-items, even in the absence of cost synergies; the latter behavior can hurt the performance of the auction. It is an empirical question whether allowing package bids and running a CA improves performance in a given setting.Analyzing the actual performance of a CA requires evaluating cost efficiency and the margins of the winning bidders, which is typically private and sensitive information of the bidders. Thus motivated, in Chapter 2 of this dissertation, we develop a structural estimation approach for large-scale first-price CAs to estimate the firms' cost structure using the bid data. To overcome the computational difficulties arising from the large number of bids observed in large-scale CAs, we propose a novel simplified model of bidders' behavior based on pricing package characteristics. Overall, this work develops the first practical tool to empirically evaluate the performance of large-scale first-price CAs commonly used in procurement settings.In Chapter 3, we apply our method to the Chilean school meals auction, in which the government procures half a billion dollars' worth of meal services every year and bidders submit thousands of package bids. Our estimates suggest that bidders' cost synergies are economically significant in this application (~5%), and the current CA mechanism achieves high allocative efficiency (~98%) and reasonable margins for the bidders (~5%). We believe this is the first work in the literature that empirically shows that a CA performs well in a real-world application.We also conduct a counterfactual analysis to study the performance of the Vickrey-Clarke-Groves (VCG) mechanism in our empirical application. While it is well known in the literature that the VCG mechanism achieves allocative efficiency, its application in practice is at best rare due to several potential weaknesses such as prohibitively high procurement costs. Interestingly, contrary to the recent theoretical work, the results show that the VCG mechanism achieves reasonable procurement costs in our application. Motivated from this observation, Chapter 4 addresses such apparent paradox between the theory and our empirical application. Focusing on the high procurement cost issue, we study the impact of competition on the revenue performance of the VCG mechanism using an asymptotic analysis. We believe the findings in this chapter add useful insights for the practical usage of the VCG mechanism

Delivering services by building and running virtual organisations

Non peer reviewedPostprin

Understanding preferences: "demand types", and the existence of equilibrium with indivisibilities

We propose new techniques for understanding agents' valuations. Our classification into \demand types", incorporates existing definitions (substitutes, complements, \strong substitutes", etc.) and permits new ones. Our Unimodularity Theorem generalises previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a \demand type" for indivisible goods. Contrary to popular belief, equilibrium is guaranteed for more classes of purely-complements, than of purely-substitutes, preferences. Our Intersection Count Theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects. Applications include matching and coalition-formation; and the Product-Mix Auction, introduced by the Bank of England in response to the financial crisis

Combinatorial auction for transportation matching service: Formulation and adaptive large neighborhood search heuristic

National Research Foundation (NRF) Singapore under Corp Lab @ Universit

Two Applications of Intelligent Transportation System.

We consider here two essential technologies of Intelligent Transportation System (ITS): Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) communication. In Chapter II, we present a method to automatically control a platoon of vehicles equipped with V2V devices. One of the major issues with platoon control is latency in wireless communications. Latency has a negative impact on safety and disrupts the stability of platoons. We propose a decentralized longitudinal platoon-controlling mechanism that uses a Model Predictive Control (MPC) approach to ensure vehicles safety, even in high-latency communications environments. The sensitivity of this method is analyzed to derive the conditions for the safety of the vehicles in the platoon. A simulation test bed for this control method is implemented to test its effectiveness and safety under two communications latency settings. The results show that the model predictive control method can safely control the platoon even in high-latency communications environments. In Chapter III, we propose a combinatorial auction implemented via a V2I system to toll and allocate traffic to eliminate congestion on a sub-network of links. We design a Vickrey-Clarke-Groove (VCG) type auction mechanism, which enables vehicles to bid for paths through V2I devices before entering the network. Using the individual vehicle bids, an optimization problem is formulated and solved, to generate the assignment of vehicles to paths and the corresponding tolls. The underlying model is analyzed for its special properties. We prove that this auction mechanism guarantees truthful reporting and maximizes the social utility. We then test this auction mechanism in two numerical experiments: first with a network of 6 links and 5100 vehicles, and then in a network with 98 links and 12000 vehicles. We prove that in a multiple origin-destination network, it is necessary to add an additional free path for each origin destination pair, in order to guarantee that the toll is always no greater than the bid made by the vehicle. We also discuss various implementation issues of this model, including use of a rolling horizon for multiple-round auctions, and the potential of this auction system as a toll setting mechanism for High-Occupancy Vehicle (HOV) or (High-Occupancy Tolled) HOT lanes.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/102386/1/haozhou_1.pd