DOCSLIB.ORG

Complexity of Hedonic Games with Dichotomous Preferences

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Complexity of Hedonic Games with Dichotomous Preferences Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence (AAAI-16) Complexity of Hedonic Games with Dichotomous Preferences Dominik Peters Department of Computer Science University of Oxford, UK [email protected] Abstract SW PF PO NS IS CR SCR p ∗ Hedonic games provide a model of coalition formation Boolean NP-c. NP-c. NP-h. NP-c. P FNP-h. Σ2-c. in which a set of agents is partitioned into coalitions 1-lists NP-c. P P P P P NP-c. and the agents have preferences over which set they be- long to. Recently, Aziz et. al. (2014) have initiated the 2-lists NP-c. P P P P P NP-c. study of hedonic games with dichotomous preferences, 3-lists NP-c. NP-c. NP-h. ? P P NP-c. where each agent either approves or disapproves of a 4-lists NP-c. NP-c. NP-h. NP-c. P P NP-c. given coalition. In this work, we study the computa- ∗ tional complexity of questions related to finding opti- Anonymous NP-c. NP-c. NP-h. NP-c. P P NP-c. mal and stable partitions in dichotomous hedonic games Intervals P P P ? P P ? under various ways of restricting and representing the Roommates P P P∗ NP-c. P P P∗ collection of approved coalitions. Encouragingly, many of these problems turn out to be polynomial-time solv- Majority ? P ? P P P P able. In particular, we show that an individually stable outcome always exists and can be found in polynomial Table 1: Overview of complexity results for various dichoto- time. We also provide efficient algorithms for cases in mous preference representations; results marked (∗) were which agents approve only few coalitions, in which they obtained elsewhere. The columns describe the problems of only approve intervals, and in which they only approve maximising welfare, and of finding (respectively) perfect, sets of size 2 (the roommates case). These algorithms pareto-optimal, Nash-stable, individually stable, core-stable, are complemented by NP-hardness results, especially and strict-core-stable partitions. for representations that are very expressive, such as in the case when agents’ goals are given by propositional formulas. optimal, or fair has turned out to be intractable even for a large variety of severely restricted preference structures. Introduction Recently, Peters and Elkind (2015) have shown that decid- ing whether a given hedonic game admits any stable outcome A coalition is an alliance between a group of individuals, at all is NP-hard for preference restrictions and representa- formed in order to achieve a common goal. How do such tions that allow agents to express more than 4 or 5 preference coalitions form if agents are selfish? An extensive literature ‘intensities’ (with some mild additional qualifiers). A result in economics and computer science has studied this question of Deineko and Woeginger (2013) shows this to also be the using the natural model of a hedonic game (see the survey case for a specific restriction allowing 3 intensities. These byAziz and Savani (2016)). A hedonic game consists of a set results suggest that if we want to stand a chance of finding of agents, each of which submits a preference ordering over polynomial time algorithms for a restricted class of hedonic all possible coalitions this agent could join. An outcome of games, we will need to go all the way down to dichotomous the game is a partition of the agent set into disjoint coalitions. preferences, which allow only 2 preference intensities. If agents are selfish, we want to find a stable outcome, while in other situations a welfare-optimal or fair outcome might In the context of hedonic games, studying the restriction to be desired. dichotomous preferences has recently been proposed by Aziz There have turned out to be multiple obstacles to achieving et al. (2014). They represent agents’ preferences by formulas these tasks. First, not all hedonic games admit any stable of propositional logic. In particular, we can use the names outcome, and thus the search for one may be futile. Second, of agents as propositional variables. An agent then approves the computational problem of finding a partition that is stable, a coalition if the members of that coalition satisfy her goal formula. Accordingly, they term games with this preference Copyright c 2016, Association for the Advancement of Artificial representation “boolean hedonic games”. Intelligence (www.aaai.org). All rights reserved. This logic representation is attractive in that it is univer- 579 sally expressive for dichotomous preferences and often suc- Preliminaries cinct. A further advantage is that we may use it to translate A hedonic game N,(i)i∈N is given by a finite set N of computational questions such as “find a stable partition” into i ∈ N propositional logic, and then use an off-the-shelf SAT solver agents, and for each agent a complete and transitive preference relation over Ni = {S ⊆ N : i ∈ S}.We to answer it. Such a translation is presented in detail by Aziz ∼ et al. (2014). Note that for some solution concepts, they write i and i for the strict and indifference parts of i. A hedonic game has dichotomous preferences, and is called have not found polynomial-size expressions. Still, given the i ∈ N impressive performance of modern SAT solvers on instances a dichotomous hedonic game, if for each agent , the coalitions Ni = {S ⊆ N : i ∈ S} can be partitioned arising in practice, we might hope that this approach allows + into approved coalitions Ni and non-approved coalitions hedonic games to be applicable in practice. − Ni such that i strictly prefers approved coalitions to non- Aziz et al. (2014) argue that their specific SAT encoding approved coalitions, but is indifferent within the two groups: cannot be improved by an efficient algorithm if and only if the + − so S i T iff S ∈N and T ∈N . corresponding computational problems are NP-hard. They i i The outcome of a hedonic game is a partition π of the write that “identifying the complexity of finding partitions agent set into disjoint coalitions. We write π(i) for the coali- satisfying solution concepts for Boolean hedonic games is tion S ∈ π that contains i ∈ N. We are interested in finding therefore the most immediate direction of further research.” partitions that are stable, optimal, and/or fair. In a dichoto- In this work, we study a variety of different restrictions mous hedonic game, a partition π maximises social welfare of agents’ dichotomous preferences, and use the term “di- if it has the maximum number of agents who are in approved chotomous hedonic game” for any hedonic game in which coalitions among all partitions of N.Ifevery agent is in all agents have dichotomous preferences. an approved coalition in π, then π is called perfect (some- π Theoretically speaking, the dichotomous case is nice be- times known as wonderfully stable). A partition is Pareto- π π(i) π(i) cause every dichotomous hedonic game admits an outcome optimal if there is no partition such that i for i ∈ N π(i) π(i) i ∈ N that is simultaneously core-stable (resistant to group devia- all and i for some . Fairness can be π tions) and individually stable (resistant to deviations by any formalised using the notion of envy-freeness: a partition is i single player). This is a refinement of an observation by Aziz envy-free if there is no agent who would prefer to be in the j π(j) \{j}∪{i} π(i) et al. (2014). While the argument establishing the existence position of agent , i.e. i . of such a partition does not yield a polynomial-time algo- There are many notions of stability for a partition π in a rithm, we identify many appealing special cases in which hedonic game. We will mainly use four such concepts. A there is one. In the general case, we always can in polyno- partition π is core-stable if there is no non-empty coalition mial time find a partition that is individually stable (but not S ⊆ N with S i π(i) for all i ∈ S. Thus, every member necessarily core-stable) when given an oracle that decides of S would strictly prefer being in S to being where they whether a given coalition is approved by a given agent. have been put under π. A partition π is strict-core-stable if there is no non-empty coalition S ⊆ N with S i π(i) for We further study the computational complexity of finding all i ∈ S and S i π(i) for some i ∈ S. In both of these a partition that maximises the number of players who ap- notions, a group of agent deviates. If we restrict our attention prove it, of finding a Pareto optimal partition, and of deciding to the possibility of just a single agent deviating, we obtain whether a strict-core-stable or a Nash-stable partition exists the notion of Nash-stability. Here, no agent i prefers to join (these concepts are strengthenings of core- and individual another coalition in π, that is π(i) i π(j) ∪{i} for all j, stability). We find that these problems are all NP-hard under and also π(i) i {i}.Inanindividually stable (IS) partition, the logic representation (which is not too surprising given its no agent prefers to deviate in this way and is welcomed by expressive power) and welfare-maximisation in particular is his new coalition. Formally, an agent i IS-deviates into a inapproximable and fixed-parameter intractable. In contrast, coalition S ∈ π ∪{∅} if S i π(i) and for each j ∈ S,we we find that these problems become easy when requiring have π(j) ∪{i} j π(j).
Load more

Recommended publications
  • Pareto Optimality in Coalition Formation
    Pareto Optimality in Coalition Formation Haris Aziz NICTA and University of New South Wales, 2033 Sydney, Australia Felix Brandt∗ Technische Universit¨atM¨unchen,80538 M¨unchen,Germany Paul Harrenstein University of Oxford, Oxford OX1 3QD, United Kingdom Abstract A minimal requirement on allocative efficiency in the social sciences is Pareto op- timality. In this paper, we identify a close structural connection between Pareto optimality and perfection that has various algorithmic consequences for coali- tion formation. Based on this insight, we formulate the Preference Refinement Algorithm (PRA) which computes an individually rational and Pareto optimal outcome in hedonic coalition formation games. Our approach also leads to var- ious results for specific classes of hedonic games. In particular, we show that computing and verifying Pareto optimal partitions in general hedonic games, anonymous games, three-cyclic games, room-roommate games and B-hedonic games is intractable while both problems are tractable for roommate games, W-hedonic games, and house allocation with existing tenants. Keywords: Coalition Formation, Hedonic Games, Pareto Optimality, Computational Complexity JEL: C63, C70, C71, and C78 1. Introduction Ever since the publication of von Neumann and Morgenstern's Theory of Games and Economic Behavior in 1944, coalitions have played a central role within game theory. The crucial questions in coalitional game theory are which coalitions can be expected to form and how the members of coalitions should divide the proceeds of their cooperation. Traditionally the focus has been on the latter issue, which led to the formulation and analysis of concepts such as ∗Corresponding author Email addresses: [email protected] (Haris Aziz), [email protected] (Felix Brandt), [email protected] (Paul Harrenstein) Preprint submitted to Elsevier August 27, 2013 the core, the Shapley value, or the bargaining set.
    [Show full text]
  • Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions
    Int J Game Theory (2008) 36:537–569 DOI 10.1007/s00182-008-0117-6 ORIGINAL PAPER Deferred acceptance algorithms: history, theory, practice, and open questions Alvin E. Roth Accepted: 19 July 2007 / Published online: 29 January 2008 © Springer-Verlag 2008 Abstract The deferred acceptance algorithm proposed by Gale and Shapley (1962) has had a profound influence on market design, both directly, by being adapted into practical matching mechanisms, and, indirectly, by raising new theoretical questions. Deferred acceptance algorithms are at the basis of a number of labor market clea- ringhouses around the world, and have recently been implemented in school choice systems in Boston and New York City. In addition, the study of markets that have failed in ways that can be fixed with centralized mechanisms has led to a deeper understanding of some of the tasks a marketplace needs to accomplish to perform well. In particular, marketplaces work well when they provide thickness to the mar- ket, help it deal with the congestion that thickness can bring, and make it safe for participants to act effectively on their preferences. Centralized clearinghouses organi- zed around the deferred acceptance algorithm can have these properties, and this has sometimes allowed failed markets to be reorganized. Keywords Matching · Market design · Gale-shapley · Deferred acceptance Introduction Matching is one of the important functions of markets. Who gets which jobs, which school places, who marries whom, these help shape lives and careers. Partly for this reason, a substantial literature has grown out of the remarkable paper “College Admissions and the Stability of Marriage” that David Gale and Lloyd Prepared for Gale’s Feast: a Day in honor of the 85th birthday of David Gale, July 2007, Stony Brook.
    [Show full text]
  • Pareto-Optimality in Cardinal Hedonic Games
    Research Paper AAMAS 2020, May 9–13, Auckland, New Zealand Pareto-Optimality in Cardinal Hedonic Games Martin Bullinger Technische Universität München München, Germany [email protected] ABSTRACT number of agents, and therefore it is desirable to consider expres- Pareto-optimality and individual rationality are among the most nat- sive, but succinctly representable classes of hedonic games. This ural requirements in coalition formation. We study classes of hedo- can be established by encoding preferences by means of a complete nic games with cardinal utilities that can be succinctly represented directed weighted graph where an edge weight EG ¹~º is a cardinal by means of complete weighted graphs, namely additively separable value or utility that agent G assigns to agent ~. Still, this underlying (ASHG), fractional (FHG), and modified fractional (MFHG) hedo- structure leaves significant freedom, how to obtain (cardinal) pref- nic games. Each of these can model different aspects of dividing a erences over coalitions. An especially appealing type of preferences society into groups. For all classes of games, we give algorithms is to have the sum of values of the other individuals as the value that find Pareto-optimal partitions under some natural restrictions. of a coalition. This constitutes the important class of additively While the output is also individually rational for modified fractional separable hedonic games (ASHGs) [6]. hedonic games, combining both notions is NP-hard for symmetric In ASHGs, an agent is willing to accept an additional agent into ASHGs and FHGs. In addition, we prove that welfare-optimal and her coalition as long as her valuation of this agent is non-negative Pareto-optimal partitions coincide for simple, symmetric MFHGs, and in this sense, ASHGs are not sensitive to the intensities of single- solving an open problem from Elkind et al.
    [Show full text]
  • Optimizing Expected Utility and Stability in Role Based Hedonic Games
    Proceedings of the Thirtieth International Florida Artificial Intelligence Research Society Conference Optimizing Expected Utility and Stability in Role Based Hedonic Games Matthew Spradling University of Michigan - Flint mjspra@umflint.edu Abstract Table 1: Ex. RBHG instance with |P | =4,R= {A, B} In the hedonic coalition formation game model Roles Based r, c u (r, c) u (r, c) u (r, c) u (r, c) Hedonic Games (RBHG), agents view teams as compositions p0 p1 p2 p3 of available roles. An agent’s utility for a partition is based A, AA 2200 upon which roles she and her teammates fulfill within the A, AB 0322 coalition. I show positive results for finding optimal or sta- B,AB 3033 ble role matchings given a partitioning into teams. In set- B,BB 1111 tings such as massively multiplayer online games, a central authority assigns agents to teams but not necessarily to roles within them. For such settings, I consider the problems of op- timizing expected utility and expected stability in RBHG. I As per (Spradling and Goldsmith 2015), a Role Based He- show that the related optimization problems for partitioning donic Game (RBHG) instance consists of: are NP-hard. I introduce a local search heuristic method for • P approximating such solutions. I validate the heuristic by com- : A population of players parison to existing partitioning approaches using real-world • R: A set of roles data scraped from League of Legends games. • C: A set of compositions, where a composition c ∈ C is a multiset (bag) of roles from R. Introduction • U : P × R × C → Z defines the utility function ui(r, c) In coalition formation games, agents from a population have for each player pi.
    [Show full text]
  • The Dynamics of Europe's Political Economy
    Die approbierte Originalversion dieser Dissertation ist in der Hauptbibliothek der Technischen Universität Wien aufgestellt und zugänglich. http://www.ub.tuwien.ac.at The approved original version of this thesis is available at the main library of the Vienna University of Technology. http://www.ub.tuwien.ac.at/eng DISSERTATION The Dynamics of Europe’s Political Economy: a game theoretical analysis Ausgeführt zum Zwecke der Erlangung des akademischen Grades einer Doktorin der Sozial- und Wirtschaftswissenschaften unter der Leitung von Univ.-Prof. Dr. Hardy Hanappi Institut für Stochastik und Wirtschaftsmathematik (E105) Forschunggruppe Ökonomie Univ.-Prof. Dr. Pasquale Tridico Institut für Volkswirtschaftslehre, Universität Roma Tre eingereicht an der Technischen Universität Wien Fakultät für Mathematik und Geoinformation von Mag. Gizem Yildirim Matrikelnummer: 0527237 Hohlweggasse 10/10, 1030 Wien Wien am Mai 2017 Acknowledgements I would like to thank Professor Hardy Hanappi for his guidance, motivation and patience. I am grateful for inspirations from many conversations we had. He was always very generous with his time and I had a great freedom in my research. I also would like to thank Professor Pasquale Tridico for his interest in my work and valuable feedbacks. The support from my family and friends are immeasurable. I thank my parents and my brother for their unconditional and unending love and support. I am incredibly lucky to have great friends. I owe a tremendous debt of gratitude to Sarah Dippenaar, Katharina Schigutt and Markus Wallerberger for their support during my thesis but more importantly for sharing good and bad times. I also would like to thank Gregor Kasieczka for introducing me to jet clustering algorithms and his valuable suggestions.
    [Show full text]
  • Fractional Hedonic Games
    Fractional Hedonic Games HARIS AZIZ, Data61, CSIRO and UNSW Australia FLORIAN BRANDL, Technical University of Munich FELIX BRANDT, Technical University of Munich PAUL HARRENSTEIN, University of Oxford MARTIN OLSEN, Aarhus University DOMINIK PETERS, University of Oxford The work we present in this paper initiated the formal study of fractional hedonic games, coalition formation games in which the utility of a player is the average value he ascribes to the members of his coalition. Among other settings, this covers situations in which players only distinguish between friends and non-friends and desire to be in a coalition in which the fraction of friends is maximal. Fractional hedonic games thus not only constitute a natural class of succinctly representable coalition formation games, but also provide an interesting framework for network clustering. We propose a number of conditions under which the core of fractional hedonic games is non-empty and provide algorithms for computing a core stable outcome. By contrast, we show that the core may be empty in other cases, and that it is computationally hard in general to decide non-emptiness of the core. 1 INTRODUCTION Hedonic games present a natural and versatile framework to study the formal aspects of coalition formation which has received much attention from both an economic and an algorithmic perspective. This work was initiated by Drèze and Greenberg[1980], Banerjee et al . [2001], Cechlárová and Romero-Medina[2001], and Bogomolnaia and Jackson[2002] and has sparked a lot of follow- up work. A recent survey was provided by Aziz and Savani[2016]. In hedonic games, coalition formation is approached from a game-theoretic angle.
    [Show full text]
  • Pareto Optimality in Coalition Formation
    Pareto Optimality in Coalition Formation Haris Aziz Felix Brandt Paul Harrenstein Technische Universität München IJCAI Workshop on Social Choice and Artificial Intelligence, July 16, 2011 1 / 21 Coalition formation “Coalition formation is of fundamental importance in a wide variety of social, economic, and political problems, ranging from communication and trade to legislative voting. As such, there is much about the formation of coalitions that deserves study.” A. Bogomolnaia and M. O. Jackson. The stability of hedonic coalition structures. Games and Economic Behavior. 2002. 2 / 21 Coalition formation 3 / 21 Hedonic Games A hedonic game is a pair (N; ) where N is a set of players and = (1;:::; jNj) is a preference profile which specifies for each player i 2 N his preference over coalitions he is a member of. For each player i 2 N, i is reflexive, complete and transitive. A partition π is a partition of players N into disjoint coalitions. A player’s appreciation of a coalition structure (partition) only depends on the coalition he is a member of and not on how the remaining players are grouped. 4 / 21 Classes of Hedonic Games Unacceptable coalition: player would rather be alone. General hedonic games: preference of each player over acceptable coalitions 1: f1; 2; 3g ; f1; 2g ; f1; 3gjf 1gk 2: f1; 2gjf 1; 2; 3g ; f1; 3g ; f2gk 3: f2; 3gjf 3gkf 1; 2; 3g ; f1; 3g Partition ff1g; f2; 3gg 5 / 21 Classes of Hedonic Games General hedonic games: preference of each player over acceptable coalitions Preferences over players extend to preferences over coalitions Roommate games: only coalitions of size 1 and 2 are acceptable.
    [Show full text]
  • Matchingmarkets
    Package ‘matchingMarkets’ February 20, 2015 Version 0.1-2 Depends R (>= 2.15.2) Imports Rcpp (>= 0.11.2), lpSolve (>= 5.6.6), partitions LinkingTo Rcpp, RcppArmadillo Date 2014-08-14 Title An R package for the analysis of stable matchings Author Thilo Klein Maintainer Thilo Klein <[email protected]> Description This package implements a structural estimator to correct for the sample selection bias from observed outcomes in matching markets. It also contains R code for matching algorithms such as the deferred-acceptance algorithm for college admissions, the top-trading-cycles algorithm for house allocation and a partitioning linear program for the roommates problem. URL https://github.com/thiloklein/matchingMarkets License GPL (>= 2) | file LICENSE Repository CRAN Repository/R-Forge/Project matchingmarkets Repository/R-Forge/Revision 16 Repository/R-Forge/DateTimeStamp 2014-11-22 23:10:11 Date/Publication 2014-11-23 09:35:22 NeedsCompilation yes R topics documented: matchingMarkets-package . .2 baac00 . .4 daa..............................................6 khb .............................................8 mfx .............................................9 1 2 matchingMarkets-package plp..............................................9 stabit . 10 stabsim . 15 ttc.............................................. 17 Index 18 matchingMarkets-package An R package for the analysis of stable matchings. Description The matchingMarkets package contains R and C++ code for the estimation of structural models that correct for the sample selection bias of observed outcomes in matching markets. Matching is concerned with who transacts with whom, and how. For example, who works at which job, which students go to which school, who forms a workgroup with whom, and so on. The empirical analysis of matching markets is naturally subject to sample selection problems.
    [Show full text]
  • 15 Hedonic Games Haris Azizaand Rahul Savanib
    Draft { December 5, 2014 15 Hedonic Games Haris Azizaand Rahul Savanib 15.1 Introduction Coalitions are a central part of economic, political, and social life, and coalition formation has been studied extensively within the mathematical social sciences. Agents (be they humans, robots, or software agents) have preferences over coalitions and, based on these preferences, it is natural to ask which coalitions are expected to form, and which coalition structures are better social outcomes. In this chapter, we consider coalition formation games with hedonic preferences, or simply hedonic games. The outcome of a coalition formation game is a partitioning of the agents into disjoint coalitions, which we will refer to synonymously as a partition or coalition structure. The defining feature of hedonic preferences is that every agent only cares about which agents are in its coalition, but does not care how agents in other coali- tions are grouped together (Dr`ezeand Greenberg, 1980). Thus, hedonic preferences completely ignore inter-coalitional dependencies. Despite their relative simplicity, hedonic games have been used to model many interesting settings, such as research team formation (Alcalde and Revilla, 2004), scheduling group activities (Darmann et al., 2012), formation of coalition governments (Le Breton et al., 2008), cluster- ings in social networks (see e.g., Aziz et al., 2014b; McSweeney et al., 2014; Olsen, 2009), and distributed task allocation for wireless agents (Saad et al., 2011). Before we give a formal definition of a hedonic game, we give a standard hedonic game from the literature that we will use as a running example (see e.g., Banerjee et al.
    [Show full text]
  • Stable Matching with PCF Version 2, an Étude in Secure Computation
    Stable Matching with PCF Version 2, an Etude´ in Secure Computation A Thesis Presented to the Faculty of the School of Engineering and Applied Science University of Virginia In Partial Fulfillment of the requirements for the Degree Master of Science (Computer Science) by Benjamin Terner August 2015 To Mom Everything I am is a reflection of the woman who raised me, and everything I do is an honor to her memory. iii Abstract The classic stable-matching algorithm of Gale and Shapley and subsequent variants by, e.g., Abdulkadiroglu et al. [APR05], have been used successfully in a number of real-world scenarios, including the assignment of US medical school graduates to residency programs and students in New York, Norway, and Singapore to high schools and universities. One shortcoming of the Gale-Shapley family of matching algorithms is susceptibility to strategic manipulation by the participants. The commonly used paradigm to mitigate this shortcoming, employing a trusted third party to compute matchings explicitly, is outdated, expensive, and in some scenarios, impossible. This makes stable matching a natural problem for secure, multiparty computation (SMPC). Secure multiparty computation allows two or more mutually distrustful parties to evaluate a joint function on their inputs without revealing more information about the inputs than each player can derive from his own input and output. We use Portable Circuit Format (PCF), a compiler and interpreter for Yao’s garbled circuit protocols, to produce the first feasible, privacy-preserving protocol for stable matching. In doing so, we improve the theoretical bounds for stable matching constructions, develop global optimizations for PCF circuits, and improve garbling techniques used by PCF.
    [Show full text]
  • Issues of Fairness and Computation in Partition Problems
    Fair and Square: Issues of Fairness and Computation in Partition Problems Inaugural-Dissertation zur Erlangung des Doktorgrades der Mathematisch-Naturwissenschaftlichen Fakultät der Heinrich-Heine-Universität Düsseldorf vorgelegt von Nhan-Tam Nguyen aus Hilden Düsseldorf, Juli 2017 aus dem Institut für Informatik der Heinrich-Heine-Universität Düsseldorf Gedruckt mit der Genehmigung der Mathematisch-Naturwissenschaftlichen Fakultät der Heinrich-Heine-Universität Düsseldorf Referent: Prof. Dr. Jörg Rothe Koreferent: Prof. Dr. Edith Elkind Tag der mündlichen Prüfung: 20.12.2017 Selbstständigkeitserklärung Ich versichere an Eides Statt, dass die Dissertation von mir selbstständig und ohne unzulässige fremde Hilfe unter Beachtung der „Grundsätze zur Sicherung guter wissenschaftlicher Praxis an der Heinrich-Heine-Universität Düsseldorf“ erstellt worden ist. Desweiteren erkläre ich, dass ich eine Dissertation in der vorliegenden oder in ähnlicher Form noch bei keiner anderen Institution eingereicht habe. Teile dieser Arbeit wurden bereits in den folgenden Schriften veröffentlicht oder zur Begutach- tung eingereicht: Baumeister et al. [2014], Baumeister et al. [2017], Nguyen et al. [2015], Nguyen et al. [2018], Heinen et al. [2015], Nguyen and Rothe [2016], Nguyen et al. [2016]. Düsseldorf, 7. Juli 2017 Nhan-Tam Nguyen Acknowledgments First and foremost, I owe a debt of gratitude to Jörg Rothe, my advisor, for his positive en- couragement, understanding, patience, and for asking the right questions. I’m grateful for his guidance through the academic world. Dorothea Baumeister deserves much thanks for being my mentor and her thorough feedback. I’d like to thank Edith Elkind for agreeing to review my thesis and be part of my defense and examination, as well as for sharing the durian at AAMAS 2016 in Singapore.
    [Show full text]
  • Devising a Framework for Efficient and Accurate Matchmaking and Real-Time Web Communication
    Dartmouth College Dartmouth Digital Commons Dartmouth College Undergraduate Theses Theses and Dissertations 6-1-2016 Devising a Framework for Efficient and Accurate Matchmaking and Real-time Web Communication Charles Li Dartmouth College Follow this and additional works at: https://digitalcommons.dartmouth.edu/senior_theses Part of the Computer Sciences Commons Recommended Citation Li, Charles, "Devising a Framework for Efficient and Accurate Matchmaking and Real-time Web Communication" (2016). Dartmouth College Undergraduate Theses. 106. https://digitalcommons.dartmouth.edu/senior_theses/106 This Thesis (Undergraduate) is brought to you for free and open access by the Theses and Dissertations at Dartmouth Digital Commons. It has been accepted for inclusion in Dartmouth College Undergraduate Theses by an authorized administrator of Dartmouth Digital Commons. For more information, please contact [email protected]. Devising a framework for efficient and accurate matchmaking and real-time web communication Charles Li Department of Computer Science Dartmouth College Hanover, NH [email protected] Abstract—Many modern applications have a great need for propose and evaluate original matchmaking algorithms, and matchmaking and real-time web communication. This paper first also discuss and evaluate implementations of real-time explores and details the specifics of original algorithms for communication using existing web protocols. effective matchmaking, and then proceeds to dive into implementations of real-time communication between different clients across the web. Finally, it discusses how to apply the II. PRIOR WORK AND RELEVANT TECHNOLOGIES techniques discussed in the paper in practice, and provides samples based on the framework. A. Matchmaking: No Stable Matching Exists Consider a pool of users. What does matchmaking entail? It Keywords—matchmaking; real-time; web could be the task of finding, for each user, the best compatriot or opponent in the pool to match with, given the user’s set of I.
    [Show full text]