On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

Packing, Scheduling and Covering Problems in a Game-Theoretic Perspective

Many packing, scheduling and covering problems that were previously considered by computer science literature in the context of various transportation and production problems, appear also suitable for describing and modeling various fundamental aspects in networks optimization such as routing, resource allocation, congestion control, etc. Various combinatorial problems were already studied from the game theoretic standpoint, and we attempt to complement to this body of research. Specifically, we consider the bin packing problem both in the classic and parametric versions, the job scheduling problem and the machine covering problem in various machine models. We suggest new interpretations of such problems in the context of modern networks and study these problems from a game theoretic perspective by modeling them as games, and then concerning various game theoretic concepts in these games by combining tools from game theory and the traditional combinatorial optimization. In the framework of this research we introduce and study models that were not considered before, and also improve upon previously known results.Comment: PhD thesi

Approximation algorithms for distributed and selfish agents

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.Includes bibliographical references (p. 157-165).Many real-world systems involve distributed and selfish agents who optimize their own objective function. In these systems, we need to design efficient mechanisms so that system-wide objective is optimized despite agents acting in their own self interest. In this thesis, we develop approximation algorithms and decentralized mechanisms for various combinatorial optimization problems in such systems. First, we investigate the distributed caching and a general set of assignment problems. We develop an almost tight LP-based ... approximation algorithm and a local search ... approximation algorithm for these problems. We also design efficient decentralized mechanisms for these problems and study the convergence of the corresponding games. In the following chapters, we study the speed of convergence to high quality solutions on (random) best-response paths of players. First, we study the average social value on best response paths in basic-utility, market sharing, and cut games. Then, we introduce the sink equilibrium as a new equilibrium concept. We argue that, unlike Nash equilibria, the selfish behavior of players converges to sink equilibria and all strategic games have a sink equilibrium. To illustrate the use of this new concept, we study the social value of sink equilibria in weighted selfish routing (or weighted congestion) games and valid-utility (or submodular-utility) games. In these games, we bound the average social value on random best-response paths for sink equilibria.. Finally, we study cross-monotonic cost sharings and group-strategyproof mechanisms.(cont.) We study the limitations imposed by the cross-monotonicity property on cost-sharing schemes for several combinatorial optimization games including set cover and metric facility location. We develop a novel technique based on the probabilistic method for proving upper bounds on the budget-balance factor of cross-monotonic cost sharing schemes, deriving tight or nearly-tight bounds for these games. At the end, we extend some of these results to group-strategyproof mechanisms.by Vahab S. Mirrokni.Ph.D

The convergence time for selfish bin packing

In classic bin packing, the objective is to partition a set of n items with positive rational sizes in (0, 1] into a minimum number of subsets called bins, such that the total size of the items of each bin at most 1. We study a bin packing game where the cost of each bin is 1, and given a valid packing of the items, each item has a cost associated with it, such that the items that are packed into a bin share its cost equally. We find tight bounds on the exact worst-case number of steps in processes of convergence to pure Nash equilibria. Those are processes that are given an arbitrary packing as an initial packing. As long as there exists an item that can reduce its cost by moving from its bin to another bin, in each step, a controller selects such an item and instructs it to perform such a beneficial move. The process converges when no further beneficial moves exist. The tight function of n that we find is in Θ(n 3/2 ). This improves the previous bound of Ma et al. [14], who showed an upper bound of O(n 2)

A Study of Problems Modelled as Network Equilibrium Flows

This thesis presents an investigation into selfish routing games from three main perspectives. These three areas are tied together by a common thread that runs through the main text of this thesis, namely selfish routing games and network equilibrium flows. First, it investigates methods and models for nonatomic selfish routing and then develops algorithms for solving atomic selfish routing games. A number of algorithms are introduced for the atomic selfish routing problem, including dynamic programming for a parallel network and a metaheuristic tabu search. A piece-wise mixed-integer linear programming problem is also presented which allows standard solvers to solve the atomic selfish routing problem. The connection between the atomic selfish routing problem, mixed-integer linear programming and the multicommodity flow problem is explored when constrained by unsplittable flows or flows that are restricted to a number of paths. Additionally, some novel probabilistic online learning algorithms are presented and compared with the equilibrium solution given by the potential function of the nonatomic selfish routing game. Second, it considers multi-criteria extensions of selfish routing and the inefficiency of the equilibrium solutions when compared with social cost. Models are presented that allow exploration of the Pareto set of solutions for a weighted sum model (akin to the social cost) and the equilibrium solution. A means by which these solutions can be measured based on the Price of Anarchy for selfish routing games is also presented. Third, it considers the importance and criticality of components of the network (edges, vertices or a collection of both) within a selfish routing game and the impact of their removal. Existing network science measures and demand-based measures are analysed to assess the change in total travel time and issues highlighted. A new measure which solves these issues is presented and the need for such a measure is evaluated. Most of the new findings have been disseminated through conference talks and journal articles, while others represent the subject of papers currently in preparation

Signalisierte Netzwerkflüsse - Optimierung von Lichtsignalanlagen und Vorwegweisern und daraus resultierende Netzwerkflussprobleme

Guideposts and traffic signals are important devices for controlling inner-city traffic and their optimized operation is essential for efficient traffic flow without congestion. In this thesis, we develop a mathematical model for guideposts and traffic signals in the context of network flow theory. Guideposts lead to confluent flows where each node in the network may have at most one outgoing flow-carrying arc. The complexity of finding maximum confluent flows is studied and several polynomial time algorithms for special graph classes are developed. For traffic signal optimization, a cyclically time-expanded model is suggested which provides the possibility of the simultaneous optimization of offsets and traffic assignment. Thus, the influence of offsets on travel times can be accounted directly. The potential of the presented approach is demonstrated by simulation of real-world instances.Vorwegweiser und Lichtsignalanlagen sind wichtige Elemente zur Steuerung innerstädtischen Verkehrs und ihre optimale Nutzung ist von entscheidender Bedeutung für einen staufreien Verkehrsfluss. In dieser Arbeit werden Vorwegweiser und Lichtsignalanlagen mittels der Netzwerkflusstheorie mathematisch modelliert. Vorwegweiser führen dabei zu konfluenten Flüssen, bei denen Fluss einen Knoten des Netzwerks nur gebündelt auf einer einzigen Kante verlassen darf. Diese konfluenten Flüsse werden hinsichtlich ihrer Komplexität untersucht und es werden Polynomialzeitalgorithmen für das Finden maximaler Flüsse auf ausgewählten Graphenklassen vorgestellt. Für die Versatzzeitoptimierung von Lichtsignalanlagen wird ein zyklisch zeitexpandiertes Modell entwickelt, das die gleichzeitige Optimierung der Verkehrsumlegung ermöglicht. So kann der Einfluss geänderter Versatzzeiten auf die Fahrzeiten direkt berücksichtigt werden. Die Leistungsfähigkeit dieses Ansatzes wird mit Hilfe von Simulationen realistischer Szenarien nachgewiesen

Characterizing and Leveraging Social Phenomena in Online Networks

Social phenomena have been studied extensively in small scales by social scientists. With the increasing popularity of Web 2.0 and online social networks/media, a large amount of data on social phenomena have become available. In this dissertation we study online social phenomena such as social influence in social networks in various contexts. This dissertation has two major components: 1. Identifying and characterizing online social phenomena 2. Leveraging online social phenomena for economic and commercial purposes. We begin the dissertation by developing multi-level revenue sharing schemes for viral marketing on social networks. Viral marketing leverages social influence among users of the social network. For our proposed models, we develop results on the computational complexity, individual rationality, and potential reach of employing the Shapley value as a revenue sharing scheme. Our results indicate that under the multi-level tree-based propagation model, the Shapley value is a promising scheme for revenue sharing, whereas under other models there are computational or incentive compatibility issues that remain open. We continue with another application of social influence: social advertising. Social advertising is a new paradigm that is utilized by online social networks. Social advertising is based in the premise that social influence can be leveraged to place ads more efficiently. The goal of our work is to understand how social ads can affect click-through rates in social networks. We propose a formal model for social ads in the context of display advertising. In our model, ads are shown to users one after the other. The probability of a user clicking an ad depends on the users who have clicked this ad so far. This information is presented to users as a social cue, thus the click probability is a function of this cue. We introduce the social display optimization problem: suppose an advertiser has a contract with a publisher for showing some number (say B) impressions of an ad. What strategy should the publisher use to show these ads so as to maximize the expected number of clicks? We show hardness results for this problem and in light of the general hardness results, we develop heuristic algorithms and compare them to natural baseline ones. We then study distributed content curation on the Web. In recent years readers have turned to the social web to consume content. In other words, they rely on their social network to curate content for them as opposed to the more traditional way of relying on news editors for this purpose -- this is an implicit consequence of social influence as well. We study how efficient this is for users with limited budgets of attention. We model distributed content curation as a reader-publisher game and show various results. Our results imply that in the complete information setting, when publishers maximize their utility selfishly, distributed content curation reaches an equilibrium which is efficient, that is, the social welfare is a constant factor of that under an optimal centralized curation. Next, we initiate the study of an exchange market problem without money that is a natural generalization of the well-studied kidney exchange problem. From the practical point of view, the problem is motivated by barter websites on the Internet, e.g., swap.com, and u-exchange.com. In this problem, the users of the social network wish to exchange items with each other. A mechanism specifies for each user a set of items that she gives away, and a set of items that she receives. Consider a set of agents where each agent has some items to offer, and wishes to receive some items from other agents. Each agent would like to receive as many items as possible from the items that she wishes, that is, her utility is equal to the number of items that she receives and wishes. However, she will have a large dis-utility if she gives away more items than what she receives, because she considers such a trade to be unfair. To ensure voluntary participation (also known as individual rationality), we require the mechanism to avoid this. We consider different variants of this problem: with and without a constraint on the length of the exchange cycles and show different results including their truthfulness and individual rationality. In the other main component of this thesis, we study and characterize two other social phenomena: 1. friends vs. the crowd and 2. altruism vs. reciprocity in social networks. More specifically, we study how a social network user's actions are influenced by her friends vs. the crowd's opinion. For example, in social rating websites where both ratings from friends and average ratings from everyone is available, we study how similar one's ratings are to each other. In the next part, we aim to analyze the motivations behind users' actions on online social media over an extended period of time. We look specifically at users' likes, comments and favorite markings on their friends' posts and photos. Most theories of why people exhibit prosocial behavior isolate two distinct motivations: Altruism and reciprocity. In our work, we focus on identifying the underlying motivations behind users' prosocial giving on social media. In particular, our goal is to identify if the motivation is altruism or reciprocity. For that purpose, we study two datasets of sequence of users' actions on social media: a dataset of wall posts by users of Facebook.com, and another dataset of favorite markings by users of Flickr.com. We study the sequence of users' actions in these datasets and provide several observations on patterns related to their prosocial giving behavior