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Title: Duality theory for optimal mechanism design
Author: Giannakopoulos, Ioannis
ISNI:       0000 0004 5359 2695
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2015
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In this work we present a general duality-theory framework for revenue maximization in additive Bayesian auctions involving multiple items and many bidders whose values for the goods follow arbitrary continuous joint distributions over some multi-dimensional real interval. Although the single-item case has been resolved in a very elegant way by the seminal work of Myerson [1981], optimal solutions involving more items still remain elusive. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the natural geometric nature of the problem and highlights its connection with the theory of bipartite graph matchings. We demonstrate the power of the framework by applying it to various special monopoly settings where a seller of multiple heterogeneous goods faces a buyer with independent item values drawn from various distributions of interest, to design both exact and approximately optimal selling mechanisms. Previous optimal solutions were only known for up to two and three goods, and a very limited range of distributional priors. The duality framework is used not only for proving optimality, but perhaps more importantly, for deriving the optimal mechanisms themselves. Some of our main results include: the proposal of a simple deterministic mechanism, which we call Straight-Jacket Auction (SJA) and is defined in a greedy, recursive way through natural geometric constraints, for many uniformly distributed goods, where exact optimality is proven for up to six items and general optimality is conjectured; a scheme of sufficient conditions for exact optimality for two-good settings and general independent distributions; a technique for upper-bounding the optimal revenue for arbitrarily many goods, with an application to uniform and exponential priors; and the proof that offering deterministically all items in a single full bundle is the optimal way of selling multiple exponentially i.i.d. items.
Supervisor: Koutsoupias, Elias Sponsor: European Research Council ; European Commission ; Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Computer science (mathematics) ; Game theory,economics,social and behavioral sciences (mathematics) ; Applications and algorithms ; mechanism design ; optimal auctions ; duality ; revenue maximization ; game theory ; approximation algorithms