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Title: Market intermediation : information, computation, and incentives
Author: Gerstgrasser, Matthias
ISNI:       0000 0004 8502 9071
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2018
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Auctions are a major field of interest in game theory and in the wider mi- croeconomics area, reflected by recognitions such as Nobel prizes to William Vickrey and Paul Milgrom. The algorithmic game theory literature too pro- vides discussion of a wide range of different auction settings. But real-life markets are rarely comprised of a single monopolist facing buyers without alternative. We therefore explore market intermediation, in which we aim to match buyers and sellers to achieve some objective. While auctions have been well-explored in manifold variations, intermediation has received less attention in the literature. We aim to move beyond the independent, single-unit case and explore the limits of what can be achieved in more complex scenarios. In the first part, we look at a correlated-priors setting. We show that the revenue-optimal mechanism for this can be computed using a polynomial-time algorithm for one buyer and one seller. For two or more buyers we show that this problem is NP-hard, in contrast, but that truthful-in-expectation mechanisms can be computed using an LP in polynomial time for fixed number of buyers and sellers. In this setting we further discuss how market intermediation relates to classical auctions, as well as reverse auctions. Further motivating our results, we show that our discussion of market intermediation can lead back to useful results for both of these settings, giving an improved algorithm for the optimal two-bidder auction, and showing for the first time that a reverse auction behaves differently than an auction. In the second part, we consider an online intermediation setting, in which the market maker encounters an unknown sequence of buyers and sellers one at a time, with knowledge of their independent priors. We explore this from the point of view of online algorithms and competitive analysis, comparing against an offline adversary who knows the buyer-seller sequence in advance. For the general case, we show that the competitive ratio of the intermediary's revenue grows as the square root of the number of buyers and sellers. In contrast, we consider two settings with natural restrictions; one in which the sequence is balanced, and one in which there is an upper limit on the number of items the intermediary is allowed to hold at any one time. For both these settings we show that the competitive ratio is constant. Finally, in the third part we explore multi-unit intermediation. In this, we consider one seller and one buyer each having concave valuation of a number of items. The intermediary's aim will be to maximise welfare, while maintaining budget balance. This setting has been explored for the single- item case, along with simple reductions for divisible goods to that case. We will give a strong characterisation result as well as approximation guarantees for the multi-unit case.
Supervisor: Goldberg, Paul ; Koutsoupias, Elias Sponsor: European Research Council ; Engineering and Physical Sciences Research Council ; Austrian Academy of Sciences
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available