# Tim RoughgardenStanford University | SU · Department of Computer Science

Tim Roughgarden

## About

193

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Citations since 2017

## Publications

Publications (193)

Finding large cliques or cliques missing a few edges is a fundamental algorithmic task in the study of real-world graphs, with applications in community detection, pattern recognition, and clustering. A number of effective backtracking-based heuristics for these problems have emerged from recent empirical work in social network analysis. Given the...

We prove novel algorithmic guarantees for several online problems in the smoothed analysis model. In this model, at each time an adversary chooses an input distribution with density function bounded above by $\tfrac{1}{\sigma}$ times that of the uniform distribution; nature then samples an input from this distribution. Crucially, our results hold f...

We initiate the study of computing (near-)optimal contracts in succinctly repre4 sentable principal-agent settings. Here optimality means maximizing the principal’s expected payoff over all incentive-compatible contracts—known in economics as “second-best” solutions. We also study a natural relaxation to approximately incentive-compatible contracts...

Prior-free auctions are robust auctions that assume no distribution over bidders' valuations and provide worst-case (input-by-input) approximation guarantees. In contrast to previous work on this topic, we pursue good prior-free auctions with non-identical bidders.
Prior-free auctions can approximate meaningful benchmarks for non-identical bidders...

In distributional or average-case analysis, the goal is to design an algorithm with good-on-average performance with respect to a specific probability distribution. Distributional analysis can be useful for the study of general-purpose algorithms on "non-pathological" inputs, and for the design of specialized algorithms in applications in which the...

In “Robust Auctions for Revenue via Enhanced Competition,” T. Roughgarden, I. Talgam-Cohen, and Q. Yan revisit the classic Bulow–Klemperer result. This result compares the revenues of two well-known auction formats: the welfare-maximizing Vickrey auction and the revenue-maximizing Myerson auction. It shows that, with an extra bidder competing for t...

We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases and sales of the items. A mechanism is given prior distributions on the agents’ valuations of th...

We initiate the study of computing (near-)optimal contracts in succinctly representable principal-agent settings. Here optimality means maximizing the principal's expected payoff over all incentive-compatible contracts---known in economics as "second-best" solutions. We also study a natural relaxation to approximately incentive-compatible contracts...

We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices under a range of assumptions about the designer’s information and agents’ valuations. Our r...

We survey several unexpected connections between computational complexity and fundamental economic questions that appear unrelated to computation.

We study the problem of computing and learning non-anonymous reserve prices to maximize revenue. We first define the Maximizing Multiple Reserves (MMR) problem in single-parameter matroid environments, where the input is m valuation profiles v¹,…,vm, indexed by the same n bidders, and the goal is to compute the vector r of (non-anonymous) reserve p...

The field of optimal mechanism design enjoys a beautiful and well-developed theory, as well as several killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major search engines auction off online advertising. There are, however, some basic problems for which t...

We consider the classic principal-agent model of contract theory, in which a principal designs an outcome-dependent compensation scheme to incentivize an agent to take a costly and unobservable action. When all of the model parameters---including the full distribution over principal rewards resulting from each agent action---are known to the design...

COMPARING DIFFERENT ALGORITHMS is hard. For almost any pair of algorithms and measure of algorithm performance like running time or solution quality, each algorithm will perform better than the other on some inputs. a For example, the insertion sort algorithm is faster than merge sort on already-sorted arrays but slower on many other inputs. When t...

Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major search engines auction off online advertising. There are, however, some basic problems for which the traditio...

The goal of this article is to identify fundamental limitations on how efficiently algorithms implemented on platforms such as MapReduce and Hadoop can compute the central problems in motivating application domains, such as graph connectivity problems. We introduce an abstract model of massively parallel computation, where essentially the only rest...

Border’s theorem gives an intuitive linear characterization of the feasible interim allocation rules of a Bayesian single-item environment, and it has several applications in economic and algorithmic mechanism design. All known generalizations of Border’s theorem either restrict attention to relatively simple settings or resort to approximation. Th...

We consider the classic principal-agent model of contract theory, in which a principal designs an outcome-dependent compensation scheme to incentivize an agent to take a costly and unobservable action. When all of the model parameters---including the full distribution over principal rewards resulting from each agent action---are known to the design...

We prove that the evolution of weight vectors in online gradient descent can encode arbitrary polynomial-space computations, even in the special case of soft-margin support vector machines. Our results imply that, under weak complexity-theoretic assumptions, it is impossible to reason efficiently about the fine-grained behavior of online gradient d...

In the worst-case analysis of algorithms, the overall performance of an algorithm is summarized by its worst performance on any input. This approach has countless success stories, but there are also important computational problems --- like linear programming, clustering, online caching, and neural network training --- where the worst-case analysis...

We consider a basic problem at the interface of two fundamental fields: submodular optimization and online learning. In the online unconstrained submodular maximization (online USM) problem, there is a universe $[n]=\{1,2,...,n\}$ and a sequence of $T$ nonnegative (not necessarily monotone) submodular functions arrive over time. The goal is to desi...

In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications in machine learning, economics, and communication systems. Our main result is the first $\frac{1}{2}$-approxima...

We study the problem of setting a price for a potential buyer with a valuation drawn from an unknown distribution D. The seller has “data” about D in the form of m ≥ 1 independent and identically distributed samples, and the algorithmic challenge is to use these samples to obtain expected revenue as close as possible to what could be achieved with...

We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer’s information and agents’ valuations. Our...

Computational complexity has already had plenty to say about the computation of economic equilibria. However, understanding when equilibria are guaranteed to exist is a central theme in economic theory, seemingly unrelated to computation. In this talk we survey our main results presented at ECâ15, which show that the existence of equilibria in ma...

Designing double auctions is a complex problem, especially when there are restrictions on the sets of buyers and sellers that may trade with one another. The goal of this paper is to develop a modular approach to the design of double auctions, by relating it to the exhaustively-studied problem of designing one-sided mechanisms with a single seller...

We study the power and limitations of posted prices in markets with identical items, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer's information and agents' valuat...

In this paper we introduce a game-theoretic model for reward functions in Bitcoin mining pools. Our model consists only of an unordered history of reported shares and gives participating miners the strategy choices of either reporting or delaying when they discover a share or full solution. We defined a precise condition for incentive compatibility...

A general approach to the design of budget-balanced cost-sharing mechanisms is to use the Shapley value, applied to the given cost function, to define payments from the players to the mechanism. Is the corresponding Shapley value mechanism “optimal” in some sense? We consider the objective of minimizing worst-case inefficiency subject to a revenue...

Deferred-acceptance auctions are mechanisms whose allocation rule can be implemented using an adaptive reverse greedy algorithm. Milgrom and Segal recently introduced these auctions and proved that they satisfy remarkable incentive guarantees: in addition to being dominant strategy and incentive compatible, they are weakly group-strategyproof and c...

We consider the problem of binary prediction with expert advice in settings where experts have agency and seek to maximize their credibility. This paper makes three main contributions. First, it defines a model to reason formally about settings with selfish experts, and demonstrates that "incentive compatible" (IC) algorithms are closely related to...

Computational and economic results suggest that social welfare maximization and combinatorial auction design are much easier when bidders' valuations satisfy the "gross substitutes" condition. The goal of this paper is to evaluate rigorously the folklore belief that the main take-aways from these results remain valid in settings where the gross sub...

This survey outlines a general and modular theory for proving approximation guarantees for equilibria of auctions in complex settings. This theory complements traditional economic techniques, which generally focus on exact and optimal solutions and are accordingly limited to relatively stylized settings. We highlight three user-friendly analytical...

The price of anarchy is a measure of the inefficiency of selfish behavior that has been successfully analyzed in many applications, including network routing, resource allocation, auctions, and even models of basketball. It is defined as the worst-case ratio between the welfare of a Nash equilibrium and that of an optimal (first-best) solution. See...

This paper presents the first polynomial-time algorithm for position and matroid auction environments that learns, from samples from an unknown distribution, an auction with expected revenue arbitrarily close to the maximum possible. In contrast to most previous work, our results do not assume that the unknown distribution is regular, and require o...

We study the problem of computing and learning non-anonymous reserve prices to maximize revenue. We first define the {\sc Maximizing Multiple Reserves (MMR)} problem in single-parameter matroid environments, where the input is $m$ valuation profiles v^1,...,v^m, indexed by the same n bidders, and the goal is to compute the vector r of (non-anonymou...

Resource selection games provide a model for a diverse collection of applications where a set of resources is matched to a set of demands. Examples include routing in traffic and in telecommunication networks, service of requests on multiple parallel queues, and acquisition of services or goods with demand-dependent prices. In reality, demands are...

The goal of this paper is to identify fundamental limitations on how efficiently algorithms implemented on platforms such as MapReduce and Hadoop can compute the central problems in the motivating application domains, such as graph connectivity problems.
We introduce an abstract model of massively parallel computation, where essentially the only re...

We present an analysis framework for bounding the price of anarchy (POA) in games that have many players, as in many of the games most pertinent to computer science applications. We use this framework to demonstrate that, in many of the models in which the POA has been studied, the POA in large games is much smaller than the worst-case bound. Our f...

We study interdependent value settings and extend several results from the well-studied independent private values model to these settings. For revenue-optimal mechanism design, we give conditions under which Myerson's virtual value-based mechanism remains optimal with interdependent values. One of these conditions is robustness of the truthfulness...

We present a general framework for proving polynomial sample complexity bounds for the problem of learning from samples the best auction in a class of "simple" auctions. Our framework captures all of the most prominent examples of "simple" auctions, including anonymous and non-anonymous item and bundle pricings, with either a single or multiple buy...

Understanding when equilibria are guaranteed to exist is a central theme in economic theory, seemingly unrelated to computation. This paper shows that the existence of pricing equilibria is inextricably connected to the computational complexity of related optimization problems: demand oracles, revenue-maximization, and welfare-maximization. This re...

We consider network cost-sharing games with nonanonymous cost functions, where the cost of each edge is a submodular function of its users, and this cost is shared using the Shapley value. Nonanonymous cost functions model asymmetries between the players, which can arise from different bandwidth requirements, durations of use, services needed, and...

High triangle density-the graph property stating that a constant fraction of two-hop paths belongs to a triangle-is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove constructively that significant portions of a triangle-dense graph are contained in a disjoint union of dense, rad...

We consider a private variant of the classical allocation problem: given k goods and n agents with private valuation functions over bundles of goods, how can we allocate goods to agents to maximize social welfare? An important special case is when agents desire at most one good, and specify their (private) value for each good: in this case, the pro...

The best algorithm for a computational problem generally depends on the
"relevant inputs," a concept that depends on the application domain and often
defies formal articulation. While there is a large literature on empirical
approaches to selecting the best algorithm for a given application domain,
there has been surprisingly little theoretical ana...

This paper presents the first polynomial-time algorithm for position and
matroid auction environments that learns, from samples from an unknown bounded
valuation distribution, an auction with expected revenue arbitrarily close to
the maximum possible. In contrast to most previous work, our results apply to
arbitrary (not necessarily regular) distri...

This document collects the lecture notes from my course "Communication
Complexity (for Algorithm Designers),'' taught at Stanford in the winter
quarter of 2015. The two primary goals of the course are: 1. Learn several
canonical problems that have proved the most useful for proving lower bounds
(Disjointness, Index, Gap-Hamming, etc.). 2. Learn how...

This paper develops a general approach, rooted in statistical learning
theory, to learning an approximately revenue-maximizing auction from data. We
introduce $t$-level auctions to interpolate between simple auctions, such as
welfare maximization with reserve prices, and optimal auctions, thereby
balancing the competing demands of expressivity and...

Border's theorem gives an intuitive linear characterization of the feasible
interim allocation rules of a Bayesian single-item environment, and it has
several applications in economic and algorithmic mechanism design. All known
generalizations of Border's theorem either restrict attention to relatively
simple settings, or resort to approximation. T...

Game-theoretic models relevant for computer science applications usually
feature a large number of players. The goal of this paper is to develop an
analytical framework for bounding the price of anarchy in such models. We
demonstrate the wide applicability of our framework through instantiations for
several well-studied models, including simultaneo...

In the design and analysis of revenue-maximizing auctions, auction performance is typically measured with respect to a prior distribution over inputs. The most obvious source for such a distribution is past data. The goal of this paper is to understand how much data is necessary and sufficient to guarantee near-optimal expected revenue.
Our basic m...

An auction house cannot generally provide the optimal auction technology to every client. Instead it provides one or several auction technologies, and clients select the most appropriate (e.g., eBay provides ascending auctions or "buy-it-now" pricing). For each client the offered technology may not be optimal, but it would be too costly for clients...

We identify how to share costs locally in weighted congestion games with polynomial cost functions in order to minimize the worst-case price of anarchy (PoA). First, we prove that among all cost-sharing methods that guarantee the existence of pure Nash equilibria, the Shapley value minimizes the worst-case PoA. Second, if the guaranteed existence c...

This paper explains when and how communication and computational lower bounds for algorithms for an optimization problem translate to lower bounds on the worst-case quality of equilibria in games derived from the problem. We give three families of lower bounds on the quality of equilibria, each motivated by a different set of problems: congestion,...

We characterize the Price of Anarchy (POA) in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (cost function-independent) worst-case examples. One note...

Structured prediction tasks in machine learning involve the simultaneous
prediction of multiple labels. This is typically done by maximizing a score
function on the space of labels, which decomposes as a sum of pairwise
elements, each depending on two specific labels. Intuitively, the more pairwise
terms are used, the better the expected accuracy....

We study the problem of setting a price for a potential buyer with a valuation drawn from an unknown distribution D. The seller has "data" about D in the form of m ≥ 1 i.i.d. samples, and the algorithmic challenge is to use these samples to obtain expected revenue as close as possible to what could be achieved with advance knowledge of D.
Our first...

Optimal mechanism design enjoys a beautiful and well-developed theory, and
also a number of killer applications. Rules of thumb produced by the field
influence everything from how governments sell wireless spectrum licenses to
how the major search engines auction off online advertising. There are,
however, some basic problems for which the traditio...

Designing double auctions is a complex problem, especially when there are restrictions on the sets of buyers and sellers that may trade with one another. The goal of this paper is to develop ``black-box reductions'' from double-auction design to the exhaustively-studied problem of designing single-sided mechanisms.
We consider several desirable pro...

Deferred-acceptance auctions are auctions for binary single-parameter mechanism design problems whose allocation rule can be implemented using an adaptive reverse greedy algorithm. Milgrom and Segal [2014] recently introduced these auctions and proved that they satisfy a remarkable list of incentive guarantees: in addition to being dominant-strateg...

In this paper, we initiate the systematic study of solving linear programs
under differential privacy. The first step is simply to define the problem: to
this end, we introduce several natural classes of private linear programs that
capture different ways sensitive data can be incorporated into a linear
program. For each class of linear programs we...

We give the first black-box reduction from approximation algorithms to truthful approximation mechanisms for a non-trivial class of multi-parameter problems. Specifically, we prove that every welfare-maximization problem that admits a fully polynomial-time approximation scheme (FPTAS) and can be encoded as a packing problem also admits a truthful-i...

We consider a private variant of the classical allocation problem: given k goods and n agents with individual, private valuation functions over bundles of goods, how can we partition the goods amongst the agents to maximize social welfare? An important special case is when each agent desires at most one good, and specifies her (private) value for e...

High triangle density -- the graph property stating that most two-hop paths
belong to a triangle -- is a common signature of social networks. This paper
studies triangle-dense graphs from a structural perspective. We prove
constructively that most of the content of a triangle-dense graph is contained
in a disjoint union of radius 2 dense subgraphs....

We study optimal and approximately-optimal mechanism design questions in the interdependent values model, which generalizes the standard setting of independent and private values. We focus our attention on ex post incentive compatible and individually rational mechanisms, and develop an analog of Myerson's optimal auction theory that applies to man...

We construct prior-free auctions with constant-factor approximation guarantees with ordered bidders, in both unlimited and limited supply settings. We compare the expected revenue of our auctions on a bid vector to the monotone price benchmark, the maximum revenue that can be obtained from a bid vector using supply-respecting prices that are noninc...

We construct prior-free auctions with constant-factor approximation
guarantees with ordered bidders, in both unlimited and limited supply settings.
We compare the expected revenue of our auctions on a bid vector to the monotone
price benchmark, the maximum revenue that can be obtained from a bid vector
using supply-respecting prices that are noninc...

In a combinatorial auction (CA) with item bidding, several goods are sold simultaneously via single-item auctions. We study how the equilibrium performance of such an auction depends on the choice of the underlying single-item auction. We provide a thorough understanding of the price of anarchy, as a function of the single-item auction payment rule...

We consider a model of user engagement in social networks, where each player incurs a cost to remain engaged but derives a benefit proportional to the number of engaged neighbors. The natural equilibrium of this model corresponds to the k-core of the social network — the maximal induced subgraph with minimum degree at least k.
We study the problem...

Most results in revenue-maximizing auction design hinge on "getting the price right" --- offering goods to bidders at a price low enough to encourage a sale, but high enough to garner non-trivial revenue. Getting the price right can be hard work, especially when the seller has little or no a priori information about bidders' valuations.
A simple al...

We define smooth games of incomplete information. We prove an ’’extension theorem” for such games:price of anarchy bounds for pure Nash equilibria for all induced full-information games extendautomatically, without quantitative degradation, to all mixed-strategy Bayes-Nash equilibria withrespect to a product prior distribution over players’ prefere...

Prior-free auctions are robust auctions that assume no distribution over bidders' valuations and provide worst-case (input-by-input) approximation guarantees. In contrast to previous work on this topic, we pursue good prior-free auctions with non-identical bidders.
Prior-free auctions can approximate meaningful benchmarks for non-identical bidders...

Complements between goods--where one good takes on added value in the presence of another--have been a thorn in the side of algorithmic mechanism designers. On the one hand, complements are common in the standard motivating applications for combinatorial auctions, like spectrum license auctions. On the other, welfare maximization in the presence of...

Motivated by the problem of querying and communicating bidders' valuations in combinatorial auctions, we study how well different classes of set functions can be sketched. More formally, let f be a function mapping subsets of some ground set [n] to the non-negative real numbers. We say that f' is an α-sketch of f if for every set S, the value f'(S)...

We study resource allocation games where allocations to agents are made in proportion to their bids. We show that the existence of a potential function in the allocation space, and a virtual price function are sufficient for the convergence of better response dynamics to Nash equilibrium. Generally, resource allocation games do not admit a potentia...

We analyze the price of anarchy (POA) in a simple and practical non-truthful combinatorial auction when players have subadditive valuations for goods. We study the mechanism that sells every good in parallel with separate second-price auctions. We first prove that under a standard "no overbidding" assumption, for every subadditive valuation profile...

We resolve the worst-case price of anarchy (POA) of atomic splittable congestion games. Prior to this work, no tight bounds on the POA in such games were known, even for the simplest non-trivial special case of affine cost functions. We make two distinct contributions. On the upper-bound side, we define the framework of "local smoothness", which re...

This manuscript presents an alternative implementation of the
truthful-in-expectation mechanism of Dughmi, Roughgarden and Yan for
combinatorial auctions with weighted-matroid-rank-sum valuations. The new
implementation uses only value queries and is approximately
truthful-in-expectation, in the sense that by reporting truthfully each agent
maximiz...

Congestion games model several interesting applications, including routing and network formation games, and also possess attractive
theoretical properties, including the existence of and convergence of natural dynamics to a pure Nash equilibrium. Weighted
variants of congestion games that rely on sharing costs proportional to players’ weights do no...

We design an expected polynomial-time, truthful-in-expectation,
(1-1/e)-approximation mechanism for welfare maximization in a fundamental class
of combinatorial auctions. Our results apply to bidders with valuations that
are m matroid rank sums (MRS), which encompass most concrete examples of
submodular functions studied in this context, including...

Game theory is emerging as a popular tool for distributed control of multiagent systems. In order to take advantage of these game theoretic tools the interactions of the autonomous agents must be designed within a game theoretic environment. A central component of this game theoretic design is the assignment of a local objective function to each de...

We give several new upper and lower bounds on the worst-case severity of Braess's Paradox and the price of anarchy of selfish routing with respect to the maximum latency objective. In single-commodity networks with unrestricted latency functions, we prove that this worst-case price of anarchy is exactly n − 1, where n is the number of network verti...

We present the first monotone randomized polynomial-time approximation scheme (PTAS) for minimizing the makespan of parallel related machines (Q parallel to C(max)), the paradigmatic problem in single-parameter algorithmic mechanism design. This result immediately gives a polynomialtime, truthful (in expectation) mechanism whose approximation guara...

Tree-matching problems arise in many computational domains. The literature provides several methods for creating correspondences between labeled trees; however, by definition, tree-matching algorithms rigidly preserve ancestry. That is, once two nodes have been placed in correspondence, their descendants must be matched as well. We introduce flexib...

We show a formal duality between certain equilibrium concepts, including the correlated and coarse correlated equilibrium,
and analysis frameworks for proving bounds on the price of anarchy for such concepts. Our first application of this duality
is a characterization of the set of distributions over game outcomes to which “smoothness bounds” alway...

Braess's Paradox is the counterintuitive but well-known fact that removing edges from a network with "selfish routing" can decrease the latency incurred by traffic in an equilibrium flow. Despite the large amount of research motivated by Braess's Paradox since its discovery in 1968, little is known about whether it is a common real-world phenomenon...

We give the first black-box reduction from arbitrary approximation algorithms to truthful approximation mechanisms for a non-trivial class of multi-parameter problems. Specifically, we prove that every packing problem that admits an FPTAS also admits a truthful-in-expectation randomized mechanism that is an FPTAS. Our reduction makes novel use of s...

We characterize the price of anarchy in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (cost function-independent) worst-case examples. One noteworthy...

The current research in algorithms and complexity theory uses game theory as an important tool for modeling and reasoning about innovative computer science applications. The auction comprises two algorithms that include an allocation algorithm, which picks the highest bidder, and a payment algorithm, which uses the bids to charge payments, namely 0...

Recently, Dobzinski and Dughmi (FOCS '09) defined a class of truthful-in-expectation VCG-based mechanisms they termed maximal-in-distributional-range (MIDR). Using MIDR mechanisms, they derived the first truthful-in-expectation FPTAS for multi-unit auctions, and showed the first separation between the power of truthful-in-expectation and truthful m...

We develop and implement a collocation method to solve for an equilibrium in the dynamic legislative bargaining game of Duggan and Kalandrakis (2008). We formulate the collocation equations in a quasi-discrete version of the model, and we show that the collocation equations are locally Lipchitz continuous and directionally differentiable. In numeri...