Deterministic, Strategyproof, and Fair Cake Cutting

We study the classic cake cutting problem from a mechanism design perspective, in particular focusing on deterministic mechanisms that are strategyproof and fair. We begin by looking at mechanisms that are non-wasteful and primarily show that for even the restricted class of piecewise constant valuations there exists no direct-revelation mechanism that is strategyproof and even approximately proportional. Subsequently, we remove the non-wasteful constraint and show another impossibility result stating that there is no strategyproof and approximately proportional direct-revelation mechanism that outputs contiguous allocations, again, for even the restricted class of piecewise constant valuations. In addition to the above results, we also present some negative results when considering an approximate notion of strategyproofness, show a connection between direct-revelation mechanisms and mechanisms in the Robertson-Webb model when agents have piecewise constant valuations, and finally also present a (minor) modification to the well-known Even-Paz algorithm that has better incentive-compatible properties for the cases when there are two or three agents.Comment: A shorter version of this paper will appear at IJCAI 201

Envy, Regret, and Social Welfare Loss

Incentive compatibility (IC) is a desirable property for any auction mechanism, including those used in online advertising. However, in real world applications practical constraints and complex environments often result in mechanisms that lack incentive compatibility. Recently, several papers investigated the problem of deploying black-box statistical tests to determine if an auction mechanism is incentive compatible by using the notion of IC-Regret that measures the regret of a truthful bidder. Unfortunately, most of those methods are computationally intensive, since they require the execution of many counterfactual experiments. In this work, we show that similar results can be obtained using the notion of IC-Envy. The advantage of IC-Envy is its efficiency: it can be computed using only the auction's outcome. In particular, we focus on position auctions. For position auctions, we show that for a large class of pricing schemes (which includes e.g. VCG and GSP), IC-Envy ≥ IC-Regret (and IC-Envy = IC-Regret under mild supplementary conditions). Our theoretical results are completed showing that, in the position auction environment, IC-Envy can be used to bound the loss in social welfare due to the advertiser untruthful behavior. Finally, we show experimentally that IC-Envy can be used as a feature to predict IC-Regret in settings not covered by the theoretical results. In particular, using IC-Envy yields better results than training models using only price and value features

Reservation Exchange Markets for Internet Advertising

Internet display advertising industry follows two main business models. One model is based on direct deals between publishers and advertisers where they sign legal contracts containing terms of fulfillment for a future inventory. The second model is a spot market based on auctioning page views in real-time on advertising exchange (AdX) platforms such as DoubleClick\u27s Ad Exchange, RightMedia, or AppNexus. These exchanges play the role of intermediaries who sell items (e.g. page-views) on behalf of a seller (e.g. a publisher) to buyers (e.g., advertisers) on the opposite side of the market. The computational and economics issues arising in this second model have been extensively investigated in recent times. In this work, we consider a third emerging model called reservation exchange market. A reservation exchange is a two-sided market between buyer orders for blocks of advertisers\u27 impressions and seller orders for blocks of publishers\u27 page views. The goal is to match seller orders to buyer orders while providing the right incentives to both sides. In this work we first describe the important features of mechanisms for efficient reservation exchange markets. We then address the algorithmic problems of designing revenue sharing schemes to provide a fair division between sellers of the revenue collected from buyers. A major conceptual contribution of this work is in showing that even though both clinching ascending auctions and VCG mechanisms achieve the same outcome from a buyer perspective, however, from the perspective of revenue sharing among sellers, clinching ascending auctions are much more informative than VCG auctions

Efficiency Guarantees in Auctions with Budgets

In settings where players have a limited access to liquidity, represented in the form of budget constraints, efficiency maximization has proven to be a challenging goal. In particular, the social welfare cannot be approximated by a better factor then the number of players. Therefore, the literature has mainly resorted to Pareto-efficiency as a way to achieve efficiency in such settings. While successful in some important scenarios, in many settings it is known that either exactly one incentive-compatible auction that always outputs a Pareto-efficient solution, or that no truthful mechanism can always guarantee a Pareto-efficient outcome. Traditionally, impossibility results can be avoided by considering approximations. However, Pareto-efficiency is a binary property (is either satisfied or not), which does not allow for approximations. In this paper we propose a new notion of efficiency, called \emph{liquid welfare}. This is the maximum amount of revenue an omniscient seller would be able to extract from a certain instance. We explain the intuition behind this objective function and show that it can be 2-approximated by two different auctions. Moreover, we show that no truthful algorithm can guarantee an approximation factor better than 4/3 with respect to the liquid welfare, and provide a truthful auction that attains this bound in a special case. Importantly, the liquid welfare benchmark also overcomes impossibilities for some settings. While it is impossible to design Pareto-efficient auctions for multi-unit auctions where players have decreasing marginal values, we give a deterministic $O(\log n)$-approximation for the liquid welfare in this setting

Multi-Agent Systems for Computational Economics and Finance

In this article we survey the main research topics of our group at the University of Essex. Our research interests lie at the intersection of theoretical computer science, artificial intelligence, and economic theory. In particular, we focus on the design and analysis of mechanisms for systems involving multiple strategic agents, both from a theoretical and an applied perspective. We present an overview of our group’s activities, as well as its members, and then discuss in detail past, present, and future work in multi-agent systems

Beyond Dominant Resource Fairness: Extensions, Limitations, and Indivisibilities

We study the problem of allocating multiple resources to agents with heterogeneous demands. Technological advances such as cloud computing and data centers provide a new impetus for investigating this problem under the assumption that agents demand the resources in fixed proportions, known in economics as Leontief preferences. In a recent paper, Ghodsi et al. [2011] introduced the dominant resource fairness (DRF) mechanism, which was shown to possess highly desirable theoretical properties under Leontief preferences. We extend their results in three directions. First, we show that DRF generalizes to more expressive settings, and leverage a new technical framework to formally extend its guarantees. Second, we study the relation between social welfare and properties such as truthfulness; DRF performs poorly in terms of social welfare, but we show that this is an unavoidable shortcoming that is shared by every mechanism that satisfies one of three basic properties. Third, and most importantly, we study a realistic setting that involves indivisibilities. We chart the boundaries of the possible in this setting, contributing a new relaxed notion of fairness and providing both possibility and impossibility results.Engineering and Applied Science

Strategyproof Allocation of Multidimensional Tasks on Clusters

Στην παρουσα εργασια μελετουμε το προβλημα της δικαιης κατανομης πορων σε ενα συστημα με πολλους υπολογιστες με πολλους πορους ο καθε ενας.Οι χρηστες εχουν διαφορετικες απαιτησεις και Leontief προτιμησεις, δηλαδη απαιτουν πορους σε σταθερους λογους. Η δικαιη κατανομη πορων ειναι κεν- τρικο προβλημα στην σχεδιαση συστηματων cloud computing . Παραδοσιακες λυσεις οπως max-min fairness ανα πορο δεν δουλευουν ικανοποιητικα σε τετοια συστηματα με πολλους πορους. Επιπλεον, η αποδοτικοτητα και η δικαιοσυνη δεν ειναι τα μονα προβληματα. Ο σχεδιαστης πρεπει να λαβει υποψην τα κινητρα των χρησ των. Τα τελευταια χρονια αυτο το προβλημα εχει τραβηξει την προσοχη της κοινοτητας της αλγοριθμικης θεωριας παιγνιων. Θα μελετησουμε τα πιο σημαντικα απο- τελεσματα σχετικα με την κατανομη πολυδιαστατων πορων, ξεκινωντας απο την δουλεια των Ghodsi et al ([7]) που μελετησε το προβλημα σε συστηματα με εναν υπολογιστη με κλασματικες διεργασιες. Συνεχιζουμε με διακριτες διεργασιες σε εναν υπολογιστη, περιπτωση που μελετηθηκε απο τους Parkes et al ([13]) . Τελος μελετουμε τη δουλεια των Friedman et al ([4]) που κοιταει το προβλημα εκτελεσης διακριτων διεργασιων σε συστηματα με πολλους υπολογιστες.The present thesis focuses on the problem of fair resource allocation in a system containing multiple machines with multiple resources each. The users have heterogeneous demands and Leontief preferences, i.e. demand resources in fixed proportions. Resource allocation is a key issue in the design of cloud computing systems. Traditional solutions, like max-min fairness per resource don’t work well in this multi resource setting. Furthermore, efficiency and fairness are not the only issues here; the designer must take into account the users’ incentives. In the past couple of years this problem has received a lot of attention from the algorithmic game theory community. We review some the most important results related to multi-resource allocation, starting from the work of Ghodsi et al ([7]) that studied the problem on a single machine setting with fractional tasks. We then move on to the indivisible tasks on a single machine case, studied by Parkes et al ([13]). Finally we discuss the work of Friedman et al ([4]) that studies the problem of executing indivisible, containerized tasks on a multiple machine setting

Allocating Indivisible Goods to Strategic Agents: Pure Nash Equilibria and Fairness

We consider the problem of fairly allocating a set of indivisible goods to a set of strategic agents with additive valuation functions. We assume no monetary transfers, and therefore, a mechanism in our setting is an algorithm that takes as input the reported—rather than the true—values of the agents. Our main goal is to explore whether there exist mechanisms that have pure Nash equilibria for every instance and, at the same time, provide fairness guarantees for the allocations that correspond to these equilibria. We focus on two relaxations of envy-freeness, namely, envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX), and we positively answer the preceding question. In particular, we study two algorithms that are known to produce such allocations in the nonstrategic setting: round-robin (EF1 allocations for any number of agents) and a cut-and-choose algorithm of Plaut and Roughgarden (EFX allocations for two agents). For round-robin, we show that all of its pure Nash equilibria induce allocations that are EF1 with respect to the underlying true values, whereas for the algorithm of Plaut and Roughgarden, we show that the corresponding allocations not only are EFX, but also satisfy maximin share fairness, something that is not true for this algorithm in the nonstrategic setting! Further, we show that a weaker version of the latter result holds for any mechanism for two agents that always has pure Nash equilibria, which all induce EFX allocations