Design and analysis of auction mechanisms: algorithms and incentives

Artem Tsikiridis

Abstract: In this dissertation, we propose novel algorithms for combinatorial auction environments using an interdisciplinary approach. At the same time, we also analyze the performance of existing auction protocols and highlight design principles that allow for provable performance guarantees.In the first part of the thesis we study two forward auction paradigms with practical significance: core-selecting mechanisms and multi-unit auctions. We begin with the notion of core-selecting mechanisms, as introduced by Ausubel and Milgrom. Such mechanisms have overall good revenue guarantees, but are known to provide incentives to bidders for misreporting their preferences. Current research has focused on identifying core-selecting mechanisms with minimal incentives to deviate from truth-telling, such as Minimum-Revenue Core-Selecting (MRCS) rules, or proposing truthful mechanisms whose revenue is competitive against core outcomes. Our results contribute to both of these directions. We study the core polytope in more depth and provide new properties and insights that are of independent interest. Utilizing these properties, we then propose a truthful mechanism that is competitive against the MRCS benchmark, the first deterministic core-competitive mechanism for binary single-parameter domains. We also answer an open question from the literature, of whether there exist MRCS non-decreasing mechanisms, in the affirmative. Next, we shift our attention to multi-unit auctions, a class of auctions first studied by Vickrey. We analyze discriminatory price auctions, the natural multi-unit extension of the (non-truthful) first price auction. We consider bidders with capped-additive valuations and establish properties that capture the sources of inefficiency. We derive new lower and upper bounds on the Price of Anarchy of mixed equilibria, showing a complete characterization of inefficient equilibria and a tight upper bound for the case of two bidders. We also show that the Price of Anarchy is strictly worse for multiple bidders and we exhibit a separation result for Bayes Nash equilibria.In the second part of this dissertation, we study procurement auctions. Firstly, we study a covering problem motivated by spatial models in crowdsourcing markets, where tasks are ordered according to some geographic or temporal criterion. We propose a truthful mechanism that achieves a bounded approximation guarantee w.r.t. the optimal cost, improving upon the state of the art. For the same objective, we propose a truthful fully polynomial-time approximation scheme (FPTAS) for the case of inputs with a constant number of tasks, a generalization of the minimum knapsack problem. We then focus on the class of budget-feasible procurement auctions, in which agents can provide their service to the auctioneer fractionally or in many levels. We propose two mechanisms, one for each setting. The mechanism for divisible agents improves upon the known state of the art, whereas the mechanism for the multiple levels of service is the first truthful and budget-feasible mechanism that achieves a constant approximation for this setting.We conclude the dissertation with an extended discussion along with open problems and directions for future research in algorithmic mechanism design for auction environments.