Bargaining and Coalition Formation
|
|
- Kellie Summers
- 5 years ago
- Views:
Transcription
1 1 These slides are based largely on Chapter 18, Appendix A of Microeconomic Theory by Mas-Colell, Whinston, and Green. Bargaining and Coalition Formation Dr James Tremewan (james.tremewan@univie.ac.at) Cooperative Game Theory 1
2 Cooperative Game Theory Cooperative Games 2/23 A cooperative game is a game in which the players have complete freedom of preplay communication and can make binding agreements. In contrast, in a non-cooperative game no communication is admitted outside the formal structure of the game, and commitments must be self-enforcing, i.e. part of a subgame perfect equilibrium. There are many solution concepts in cooperative game theory, e.g: The Nash bargaining solution was an example of a solution concept for a class of cooperative games. The core includes outcomes that may result from coalitional competition (descriptive). The Shapley value is motivated as a fair division of surplus (normative).
3 3/23 Cooperative Game Theory Games in Characteristic Form Cooperative games are described in characteristic form. The characteristic form summarizes the payoffs available to different coalitions. The set of players is denoted I = 1,..., I. Nonempty subsets S, T I are coalitions. An outcome is a list of utilities u = (u 1,..., u I ) R I. The relevant coordinates for a coalition S are u S = (u i ) i S. A utility possibility set is a nonempty, closed set U S R S where u S U S and u S u S implies u S U S i.e. utility freely disposable. A game in characteristic form (I, V ) is a set of players I and a rule V ( ) that associates to evry coalition S I a utility possibility set V (S) R S.
4 4/23 Cooperative Game Theory Characteristic Form: Examples Nash bargaining game (using notation from earlier in course): I = {1, 2}; V ({1}) = d 1, V ({2}) = d 2, and V ({1, 2}) = S. Three-player example (I = {1, 2, 3}):
5 5/23 Cooperative Game Theory Superadditive Games A game is superadditive if two (non-overlapping) coalitions can do at least as well together as alone. Formally: A game in characteristic form (I, V ) is superadditive if for any coalitions S, T I such that S T = we have: if u S V (S) and u T V (T ), then (u S, u T ) V (S T ). We will look only at superadditive games: as in the bilateral section, we are primarily interested in situations where there are gains from cooperation.
6 6/23 Cooperative Game Theory Transferable Utility (TU) Much of the literature focuses on TU games (as will we), i.e. where utility can be transfered costlessly between coalition members. Sufficient conditions for TU are: Players can make side-payments. Players utility is linear in money. Excludes, for example, situations where bribes are illegal. In TU games, V (S) = {u S R S : i S u S i v(s)} for some v(s). i.e. coalition S chooses a joint action to maximise their total utility, denoted v(s) which can be allocated amongst S in any way. v(s) is called the worth of coalition S.
7 7/23 Cooperative Game Theory TU Games: Example Boundaries in TU games are hyperplanes in R S :
8 8/23 Cooperative Game Theory TU Games: Simplex Representation Normalising utilities such that V ({i}) = 0 i allows us to represent an n-player TU game on an (n-1) dimension simplex:
9 9/23 Cooperative Game Theory Two Games in Characteristic Form A three-player game is defined by: v({1, 2, 3}) = 1, v({1, 3}) = v({2, 3}) = 1, v({1, 2}) = 0, v({1}) = v({2}) = v({3}) = 0. What do you think will/should happen in this game? A three-player game is defined by: v({1, 2, 3}) = 10, v({1, 2}) = 10, v({1, 3}) = 3, v({2, 3}) = 2, v({1}) = v({2}) = v({3}) = 0. What do you think will/should happen in this game?
10 10/23 The Core The Core The set of feasible utility outcomes with the property that no coalition could improve the payoffs of all its members. In TU games the core is the set of utility vectors u = (u 1,..., u I ) such that: u i v(s) S I, and i S u i v(i ) i I The core may be: Empty (strategic instability, no useful prediction, e.g. divide-the-dollar majority rules). Large (makes no useful prediction, e.g. divide-the-dollar unanimity rules). Non-empty and small (makes sharp prediction). Note that the core depends only on ordinal utility.
11 11/23 The Core A TU Game with Non-Empty Core
12 12/23 The Core A TU Game with Empty Core
13 The Shapley Value The Shapley Value 13/23 Describes a reasonable or fair division taking as given the strategic realities captured by the characteristic form. Idea of fairness here is egalitarianism: gains from cooperation should be divided equally. Two player example (I, v) = ({1, 2}, v): Gains from cooperation = v(i ) v({1}) v({2}). Sh i (I, v) = v({i}) (v(i ) v({1}) v({2})) Can re-write as: Sh 1 (I, v) Sh 1 ({1}, v) = Sh 2 (I, v) Sh 2 ({2}, v), and Sh 1 (I, v) + Sh 2 (I, v) = v(i ), where Sh i ({i}, v) = v({i}) The benefit to player one from the presence of player two is the same as the benefit to player two from the presence of player one. Now generalize this idea to more players...
14 14/23 The Shapley Value The Shapley Value The Shapley value of a game (I, v) is the outcome consistent with: Sh i (S, v) Sh i (S\{h}, v) = Sh h (S, v) Sh h (S\{i}, v), and Sh i (S, v) = v(s), i S for every subgame (S, v) and all players i, h S. In words: the benefit a member of a coalition (player i) gets from another (player h) joining is equal to the benefit player h would get if already a member and player i was joining. This outcome is unique.
15 The Shapley Value 2 See Shapley (1953) for a precise definition. 15/23 The Shapley Value: Axioms The Shapley value can also be derived as the unique value satisfying three axioms (here loosely defined): Efficiency: i S Sh i (I, v) = v(i ), i.e. no utility is wasted. Symmetry: If (I, v) and (I, v ) are identical except the roles of players i and h are swapped, then Sh i (I, v) = Sh j (S, v ), i.e. labeling doesn t matter. Additivity: If a game is in a particular sense the sum of two other games 2, then Sh(I, v + w) = Sh(I, v) + Sh(I, w).
16 16/23 The Shapley Value The Shapley Value An easy way to calculate the Shapley value: Sh i (I, v) = s!(n s 1)! n! (v(s {i}) v(s)), i S where s = S and n = I. Intuition: imagine a coalition of all the players is formed by including one player at a time in a random order, and each player receives all of the added benefit to the coalition at the time they are included. The Shapley value is the expected value of this process if all orders are equally likely. v(s {i}) v(s) is the value the new player adds. s! is number of ways the existing members of S could have arrived. (n s 1)! is number of ways the remaining players can arrive. n! is the number of possible ways of the players arriving overall.
17 Examples Glove Market: The Shapley Value A three-player game is defined by: v({1, 2, 3}) = 1, v({1, 3}) = v({2, 3}) = 1, v({1, 2}) = 0, v({1}) = v({2}) = v({3}) = 0. Player 1: The value P1 adds to the coalition {3} is 1, and this happens only if P3 is added first, then P1 second. P1 adds 0 to any other coalition. There are six possible orderings so Sh i (I, v) = 1 6. Player 2: as for P1. 17/23
18 Examples Glove Market: The Shapley Value Player 3: adds 1 to the coalition {1} is, and this happens only if P1 is added first, then P3 second. adds 1 to the coalition {2} is, and this happens only if P2 is added first, then P3 second. adds 1 to the coalition {1, 2} is, and this happens if P1 is added first, P2 second, then P3 third, or if P2 is added first, P1 second, then P3 third. Sh 3 (I, v) = = 2 3 The Shapley value suggests the allocation { 1 6, 1 6, 2 3 } Check! The sum of Sh i (I, v) is v(i )! 18/23
19 19/23 Examples Glove Market: the Core What is the core of this game?: Consider an allocation {u 1, u 2, u 3 }. Suppose u 1 > 0. P2 and P3 are better off forming the coalition {2, 3} and sharing u 2 = u u 1 and u 3 = u u 1. Therefore in any allocation in the core u 1 = 0 (similarly u 2 = 0). No coalition can improve on {0, 0, 1} for all members. The core is {0, 0, 1}. The strategic environment means P1 and P2 undercut each other leaving zero profits. The Shapley value ({ 1, 1, 2 }) is more equitable than the core However the Shapley value is less equitable than an even split ({ 1, 1, 1 }) because it recognises to some extent the individual contributions (bargaining power?) of the different players.
20 Examples Three Player Game: The Shapley Value A three-player game is defined by: v({1, 2, 3}) = 10, v({1, 2}) = 10, v({1, 3}) = 3, v({2, 3}) = 2, v({1}) = v({2}) = v({3}) = 0. Player 1: adds 10 to the coalition {2} if P2 is added first, then P1 second. adds 3 to the coalition {3} if P3 is added first, then P1 second. adds 8 to the coalition {2, 3} if P2 is added first, P3 second and P1 third; or if P3 is added first, P2 second and P1 third. P1 adds 0 to any other coalition. There are six possible orderings so Sh 1 (I, v) = = /23
21 Examples Three Player Game: The Shapley Value 21/23 Player 2: adds 10 to the coalition {1} if P1 is added first, then P2 second. adds 2 to the coalition {3} if P3 is added first, then P2 second. adds 7 to the coalition {1, 3} if P1 is added first, P3 second and P2 third; or if P3 is added first, P1 second and P2 third. P2 adds 0 to any other coalition. Sh 2 (I, v) = = 26 6 Player 3: adds 3 to the coalition {1} if P1 is added first, then P3 second. adds 2 to the coalition {2} if P2 is added first, then P3 second. adds 3 to the coalition {1, 2} if P1 is added first, P2 second and P3 third; or if P2 is added first, P1 second and P3 third. P3 adds 0 to any other coalition. Sh 3 (I, v) = = 5 6 The Shapley value suggests the allocation { 29 6, 26 6, 5 6 }
22 22/23 Examples Three Player Game: The Core Consider an allocation {u 1, u 2, u 3 }. If u 1 + u 2 < 10 P1 and P2 are better off forming the coalition {1, 2} and sharing u 1 = u (10 u 1 u 2 ) and u 2 = u (10 u 1 u 2 ). Therefore in any allocation in the core u 1 + u But v(i ) = 10 so u 1 + u 2 10 which means u 1 + u 2 = 10. Thus u 3 = 0 (from now on we take this as given). If u 1 < 3 P1 is better off forming the coalition {1, 3} and sharing u 1 = u 1 + ɛ, u 3 = 3 u 1 ɛ. If u 2 < 2 P2 is better off forming the coalition {2, 3} and sharing u 2 = u 2 + ɛ, u 3 = 2 u 2 ɛ. The core is the set of allocations {x, 10 x, 0} where x [3, 8].
23 23/23 Three Player Game Examples (0,10,0). (3,7,0) Shapley value Core (8,2,0).... (0,0,10) (10,0,0)
Interactive Geometry for Surplus Sharing in Cooperative Games
Utah State University DigitalCommons@USU Applied Economics Faculty Publications Applied Economics 2006 Interactive Geometry for Surplus Sharing in Cooperative Games Arthur J. Caplan Utah State University
More informationCore Membership Computation for Succinct Representations of Coalitional Games
Core Membership Computation for Succinct Representations of Coalitional Games Xi Alice Gao May 11, 2009 Abstract In this paper, I compare and contrast two formal results on the computational complexity
More informationCooperative Games. Lecture 1: Introduction. Stéphane Airiau. ILLC - University of Amsterdam
Cooperative Games Lecture 1: Introduction Stéphane Airiau ILLC - University of Amsterdam Stéphane Airiau (ILLC) - Cooperative Games Lecture 1: Introduction 1 Why study coalitional games? Cooperative games
More informationCost-allocation Models in Electricity Systems
8 Cost-allocation Models in Electricity Systems Presented by Athena Wu Supervisor: Andy Philpott Co-supervisor: Golbon Zakeri Cost Recovery Problem Extract payments for shared resource Public utility cost
More informationStochastic Coalitional Games with Constant Matrix of Transition Probabilities
Applied Mathematical Sciences, Vol. 8, 2014, no. 170, 8459-8465 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.410891 Stochastic Coalitional Games with Constant Matrix of Transition Probabilities
More information(67686) Mathematical Foundations of AI July 30, Lecture 11
(67686) Mathematical Foundations of AI July 30, 2008 Lecturer: Ariel D. Procaccia Lecture 11 Scribe: Michael Zuckerman and Na ama Zohary 1 Cooperative Games N = {1,...,n} is the set of players (agents).
More informationMAY 2009 EXAMINATIONS. Multiagent Systems
COMP310 DEPARTMENT : Computer Science Tel. No. 7790 MAY 2009 EXAMINATIONS Multiagent Systems TIME ALLOWED : Two and a Half hours INSTRUCTIONS TO CANDIDATES Answer four questions. If you attempt to answer
More informationCHAPTER 13: FORMING COALITIONS. Multiagent Systems. mjw/pubs/imas/
CHAPTER 13: FORMING COALITIONS Multiagent Systems http://www.csc.liv.ac.uk/ mjw/pubs/imas/ Coalitional Games Coalitional games model scenarios where agents can benefit by cooperating. Issues in coalitional
More informationCAP 5993/CAP 4993 Game Theory. Instructor: Sam Ganzfried
CAP 5993/CAP 4993 Game Theory Instructor: Sam Ganzfried sganzfri@cis.fiu.edu 1 Announcements HW 1 due today HW 2 out this week (2/2), due 2/14 2 Definition: A two-player game is a zero-sum game if for
More informationSolutions of Stochastic Coalitional Games
Applied Mathematical Sciences, Vol. 8, 2014, no. 169, 8443-8450 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.410881 Solutions of Stochastic Coalitional Games Xeniya Grigorieva St.Petersburg
More informationA TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS
Iranian Journal of Fuzzy Systems Vol. 5, No. 7, 208 pp. 2-3 2 A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS A. C. CEVIKEL AND M. AHLATCIOGLU Abstract. In this paper,
More informationNash Equilibrium Load Balancing
Nash Equilibrium Load Balancing Computer Science Department Collaborators: A. Kothari, C. Toth, Y. Zhou Load Balancing A set of m servers or machines. A set of n clients or jobs. Each job can be run only
More informationOptimal Routing Control: Repeated Game Approach
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 47, NO. 3, MARCH 2002 437 Optimal Routing Control: Repeated Game Approach Richard J. La and Venkat Anantharam, Fellow, IEEE Abstract Communication networks
More informationToday s lecture. Competitive Matrix Games. Competitive Matrix Games. Modeling games as hybrid systems. EECE 571M/491M, Spring 2007 Lecture 17
EECE 57M/49M, Spring 007 Lecture 7 Modeling games as hybrid systems oday s lecture Background Matrix games Nash Competitive Equilibrium Nash Bargaining Solution Strategy dynamics: he need for hybrid models
More informationInternet Economics: The Use of Shapley Value for ISP Settlement
IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 18, NO. 3, JUNE 2010 775 Internet Economics: The Use of Shapley Value for ISP Settlement Richard T. B. Ma, Dah Ming Chiu, Fellow, IEEE, John C. S. Lui, Fellow,
More information15-451/651: Design & Analysis of Algorithms October 11, 2018 Lecture #13: Linear Programming I last changed: October 9, 2018
15-451/651: Design & Analysis of Algorithms October 11, 2018 Lecture #13: Linear Programming I last changed: October 9, 2018 In this lecture, we describe a very general problem called linear programming
More informationComputing cooperative solution concepts in coalitional skill games
Computing cooperative solution concepts in coalitional skill games The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation
More informationStrategic Network Formation
Strategic Network Formation Sanjeev Goyal Christ s College University of Cambridge Indian Institute of Science Bangalore Outline 1. Structure of networks 2. Strategic foundations of networks 3. Theory
More informationThe Shapley value mechanism for ISP settlement
The Shapley value mechanism for ISP settlement Richard T.B. Ma Dept. of Electrical Engineering Columbia University tbma@ee.columbia.edu Vishal Misra Dept. of Computer Science Columbia University misra@cs.columbia.edu
More informationInteractive Geometry for Surplus Sharing in Cooperative Games
DigitalCommons@USU Economic Research Institute Study Papers Economics and Finance 2005 Interactive Geometry for Surplus Sharing in Cooperative Games Arthur J. Caplan Yuya Sasaki Follow this and additional
More informationComment on Strategic Information Management Under Leakage in a. Supply Chain
Comment on Strategic Information Management Under Leakage in a Supply Chain Lin Tian 1 School of International Business Administration, Shanghai University of Finance and Economics, 00433 Shanghai, China,
More informationModeling Social and Economic Exchange in Networks
Modeling Social and Economic Exchange in Networks Cornell University Joint work Éva Tardos (Cornell) Networks Mediate Exchange U.S. electric grid High-school dating (Bearman-Moody-Stovel 2004) Networks
More informationNetwork Formation Games and the Potential Function Method
CHAPTER 19 Network Formation Games and the Potential Function Method Éva Tardos and Tom Wexler Abstract Large computer networks such as the Internet are built, operated, and used by a large number of diverse
More informationNetwork Topology and Equilibrium Existence in Weighted Network Congestion Games
Network Topology and Equilibrium Existence in Weighted Network Congestion Games Igal Milchtaich, Bar-Ilan University August 2010 Abstract. Every finite noncooperative game can be presented as a weighted
More informationAM 221: Advanced Optimization Spring 2016
AM 221: Advanced Optimization Spring 2016 Prof Yaron Singer Lecture 3 February 1st 1 Overview In our previous lecture we presented fundamental results from convex analysis and in particular the separating
More informationIntroduction to Game Theory
Lecture Introduction to Game Theory March 30, 005 Lecturer: Anna R. Karlin Notes: Atri Rudra In this course we will look at problems and issues which fall in the intersection of Computer Science and Economics.
More informationA Game-Theoretic Framework for Congestion Control in General Topology Networks
A Game-Theoretic Framework for Congestion Control in General Topology SYS793 Presentation! By:! Computer Science Department! University of Virginia 1 Outline 2 1 Problem and Motivation! Congestion Control
More informationAlgorithmic Game Theory and Applications. Lecture 16: Selfish Network Routing, Congestion Games, and the Price of Anarchy.
Algorithmic Game Theory and Applications Lecture 16: Selfish Network Routing, Congestion Games, and the Price of Anarchy Kousha Etessami games and the internet Basic idea: The internet is a huge experiment
More informationMath 5593 Linear Programming Lecture Notes
Math 5593 Linear Programming Lecture Notes Unit II: Theory & Foundations (Convex Analysis) University of Colorado Denver, Fall 2013 Topics 1 Convex Sets 1 1.1 Basic Properties (Luenberger-Ye Appendix B.1).........................
More informationCDG2A/CDZ4A/CDC4A/ MBT4A ELEMENTS OF OPERATIONS RESEARCH. Unit : I - V
CDG2A/CDZ4A/CDC4A/ MBT4A ELEMENTS OF OPERATIONS RESEARCH Unit : I - V UNIT I Introduction Operations Research Meaning and definition. Origin and History Characteristics and Scope Techniques in Operations
More informationAbstract Combinatorial Games
Abstract Combinatorial Games Arthur Holshouser 3600 Bullard St. Charlotte, NC, USA Harold Reiter Department of Mathematics, University of North Carolina Charlotte, Charlotte, NC 28223, USA hbreiter@email.uncc.edu
More informationOptimal Channel Selection for Cooperative Spectrum Sensing Using Coordination Game
2012 7th International ICST Conference on Communications and Networking in China (CHINACOM) Optimal Channel Selection for Cooperative Spectrum Sensing Using Coordination Game Yuhua Xu, Zhan Gao and Wei
More information1 Non greedy algorithms (which we should have covered
1 Non greedy algorithms (which we should have covered earlier) 1.1 Floyd Warshall algorithm This algorithm solves the all-pairs shortest paths problem, which is a problem where we want to find the shortest
More informationAdvanced Operations Research Techniques IE316. Quiz 1 Review. Dr. Ted Ralphs
Advanced Operations Research Techniques IE316 Quiz 1 Review Dr. Ted Ralphs IE316 Quiz 1 Review 1 Reading for The Quiz Material covered in detail in lecture. 1.1, 1.4, 2.1-2.6, 3.1-3.3, 3.5 Background material
More informationEnd-to-end QoS negotiation in network federations
End-to-end QoS negotiation in network federations H. Pouyllau, R. Douville Avril, 2010 Outline Motivation for Network federations The problem of end-to-end SLA composition Scenario of composition and negotiation
More informationEfficiency and stability in electrical power transmission networks
Efficiency and stability in electrical power transmission networks A partition function form approach Dávid Csercsik 1 László Á. Kóczy 12 koczy@krtk.mta.hu 1 Research Centre for Economic and Regional Studies,
More information6 Extensive Form Games
6 Extensive Form Games 6.1 Example: Representing a Simultaneous 22 Game Alice H HHHH O H HH o Q Bob H QQQ h o HHHH h 2 1 1 2 Figure 1: The Battle of the Sexes in Extensive Form So far we have described
More informationA Cooperative Game Theory Approach to Resource Allocation in Wireless ATM Networks
A Cooperative Game Theory Approach to Resource Allocation in Wireless ATM Networks Xinjie Chang 1 and Krishnappa R. Subramanian Network Technology Research Center, School of EEE, Nanyang Technological
More informationLiterature survey on game-theoretic approaches in cooperative networks
1 Literature survey on game-theoretic approaches in cooperative networks Chuan-Zheng Lee Abstract We conduct a literature survey of three papers applying game theory to study incentives in cooperative
More informationBasic Graph Theory with Applications to Economics
Basic Graph Theory with Applications to Economics Debasis Mishra February 6, What is a Graph? Let N = {,..., n} be a finite set. Let E be a collection of ordered or unordered pairs of distinct elements
More informationRepresentation of Finite Games as Network Congestion Games
Representation of Finite Games as Network Congestion Games Igal Milchtaich To cite this version: Igal Milchtaich. Representation of Finite Games as Network Congestion Games. Roberto Cominetti and Sylvain
More informationBeyond Minimax: Nonzero-Sum Game Tree Search with Knowledge Oriented Players
Beyond Minimax: Nonzero-Sum Game Tree Search with Knowledge Oriented Players Tian Sang & Jiun-Hung Chen Department of Computer Science & Engineering University of Washington AAAI Metareasoning Workshop,
More informationDynamics, stability, and foresight in the Shapley-Scarf housing market. Discussion Paper No
Dynamics, stability, and foresight in the Shapley-Scarf housing market Yoshio Kamijo Ryo Kawasaki Discussion Paper No. 2008-12 October 2008 Dynamics, stability, and foresight in the Shapley-Scarf housing
More informationDISJOINTNESS OF FUZZY COALITIONS
DISJOINTNESS OF FUZZY COALITIONS (Discussion) Milan Mareš Prague Milan Vlach Kyoto ÚTIA AV ČR, Pod vodárenskou věží 4, 182 08 Praha 8, Czech Republic, mares@utia.cas.cz The Kyoto College of Graduate Studies
More informationLecture 1: Sperner, Brouwer, Nash. Philippe Bich, PSE and University Paris 1 Pantheon-Sorbonne, France. Lecture 1: Sperner, Brouwer, Nash
.., PSE and University Paris 1 Pantheon-Sorbonne, France. 1. Simplex A n-simplex (or simplex of dimension n) is (x 0,...x n ) = { n i=0 λ ix i : (λ 0,..., λ n ) R n+1 + : n i=0 λ i = 1}, where x 0,...,
More informationOn the Efficiency of Negligence Rule
Jawaharlal Nehru University From the SelectedWorks of Satish K. Jain 2009 On the Efficiency of Negligence Rule Satish K. Jain, Jawaharlal Nehru University Available at: https://works.bepress.com/satish_jain/2/
More informationCONSUMPTION BASICS. MICROECONOMICS Principles and Analysis Frank Cowell. July 2017 Frank Cowell: Consumption Basics 1
CONSUMPTION BASICS MICROECONOMICS Principles and Analysis Frank Cowell July 2017 Frank Cowell: Consumption Basics 1 Overview Consumption: Basics The setting The environment for the basic consumer optimisation
More informationVertical Handover Decision Strategies A double-sided auction approach
Vertical Handover Decision Strategies A double-sided auction approach Working paper Hoang-Hai TRAN Ph.d student DIONYSOS Team INRIA Rennes - Bretagne Atlantique 1 Content Introduction Handover in heterogeneous
More information1.1 What is Microeconomics?
1.1 What is Microeconomics? Economics is the study of allocating limited resources to satisfy unlimited wants. Such a tension implies tradeoffs among competing goals. The analysis can be carried out at
More informationProject: A survey and Critique on Algorithmic Mechanism Design
Project: A survey and Critique on Algorithmic Mechanism Design 1 Motivation One can think of many systems where agents act according to their self interest. Therefore, when we are in the process of designing
More informationOn Agent Types in Coalition Formation Problems
On Agent Types in Coalition Formation Problems Tammar Shrot 1, Yonatan Aumann 1, and Sarit Kraus 1, 1 Department of Computer Science Institute for Advanced Computer Studies Bar Ilan University University
More informationDealing With Misbehavior In Distributed Systems: A Game-Theoretic Approach
Wayne State University DigitalCommons@WayneState Wayne State University Dissertations 1-1-2010 Dealing With Misbehavior In Distributed Systems: A Game-Theoretic Approach Nandan Garg Wayne State University,
More informationMathematical Themes in Economics, Machine Learning, and Bioinformatics
Western Kentucky University From the SelectedWorks of Matt Bogard 2010 Mathematical Themes in Economics, Machine Learning, and Bioinformatics Matt Bogard, Western Kentucky University Available at: https://works.bepress.com/matt_bogard/7/
More informationCHAPTER 8. Copyright Cengage Learning. All rights reserved.
CHAPTER 8 RELATIONS Copyright Cengage Learning. All rights reserved. SECTION 8.3 Equivalence Relations Copyright Cengage Learning. All rights reserved. The Relation Induced by a Partition 3 The Relation
More informationUncertainty Regarding Interpretation of the `Negligence Rule' and Its Implications for the Efficiency of Outcomes
Jawaharlal Nehru University From the SelectedWorks of Satish K. Jain 2011 Uncertainty Regarding Interpretation of the `Negligence Rule' and Its Implications for the Efficiency of Outcomes Satish K. Jain,
More informationMath 302 Introduction to Proofs via Number Theory. Robert Jewett (with small modifications by B. Ćurgus)
Math 30 Introduction to Proofs via Number Theory Robert Jewett (with small modifications by B. Ćurgus) March 30, 009 Contents 1 The Integers 3 1.1 Axioms of Z...................................... 3 1.
More informationLecture 2. Sequential Equilibrium
ECON601 Spring, 2015 UBC Li, Hao Lecture 2. Sequential Equilibrium Strategies and beliefs Applying idea of subgame perfection of extensive games with perfect information to extensive games with imperfect
More information16 th Polish Teletraffic Symposium 2009 Łódź, Poland, September 24-25, 2009
MARIUSZ MYCEK Institute of Telecommunications, Warsaw University of Technology, Poland MICHAŁ PIÓRO Institute of Telecommunications, Warsaw University of Technology, Poland Department of Electrical and
More informationA Network Coloring Game
A Network Coloring Game Kamalika Chaudhuri, Fan Chung 2, and Mohammad Shoaib Jamall 2 Information Theory and Applications Center, UC San Diego kamalika@soe.ucsd.edu 2 Department of Mathematics, UC San
More informationMigrating to IPv6 The Role of Basic Coordination
Migrating to IPv6 The Role of Basic Coordination M. Nikkhah Dept. Elec. & Sys. Eng. University of Pennsylvania R. Guérin Dept. Comp. Sci. & Eng. Washington U. in St. Louis Outline Background and Motivations
More informationA Fair Cooperative Content-Sharing Service
A Fair Cooperative Content-Sharing Service L.Militano a,, A.Iera a, F.Scarcello b a University Mediterranea of Reggio Calabria, DIIES Department, Italy b University della Calabria, Cosenza, DIMES Department,
More informationAXIOMS FOR THE INTEGERS
AXIOMS FOR THE INTEGERS BRIAN OSSERMAN We describe the set of axioms for the integers which we will use in the class. The axioms are almost the same as what is presented in Appendix A of the textbook,
More informationIntroduction to Dynamic Traffic Assignment
Introduction to Dynamic Traffic Assignment CE 392D January 22, 2018 WHAT IS EQUILIBRIUM? Transportation systems involve interactions among multiple agents. The basic facts are: Although travel choices
More informationThroughput Enhancement for Wireless Networks using Coalition Formation Game
Throughput Enhancement for Wireless Networks using Coalition Formation Game 9 Dec. 22, 2011 Abstract With the limited wireless spectrum and the ever-increasing demand for wireless services, enhancing the
More informationEC422 Mathematical Economics 2
EC422 Mathematical Economics 2 Chaiyuth Punyasavatsut Chaiyuth Punyasavatust 1 Course materials and evaluation Texts: Dixit, A.K ; Sydsaeter et al. Grading: 40,30,30. OK or not. Resources: ftp://econ.tu.ac.th/class/archan/c
More informationIntegrated Security Services for Dynamic Coalition Management
Center for Satellite and Hybrid Communication Networks Integrated Security Services for Dynamic Coalition Management Virgil D. Gligor and John S. Baras Electrical and Computer Engineering Department, University
More informationJoint Entity Resolution
Joint Entity Resolution Steven Euijong Whang, Hector Garcia-Molina Computer Science Department, Stanford University 353 Serra Mall, Stanford, CA 94305, USA {swhang, hector}@cs.stanford.edu No Institute
More informationClassroom Tips and Techniques: Nonlinear Curve Fitting. Robert J. Lopez Emeritus Professor of Mathematics and Maple Fellow Maplesoft
Classroom Tips and Techniques: Nonlinear Curve Fitting Robert J. Lopez Emeritus Professor of Mathematics and Maple Fellow Maplesoft Introduction I was recently asked for help in fitting a nonlinear curve
More informationCOALITION FORMATION IN P2P FILE SHARING SYSTEMS
COALITION FORMATION IN P2P FILE SHARING SYSTEMS M.V.Belmonte, M. Díaz, J.L. Pérez-de-la-Cruz, R. Conejo E.T.S.I. Informática. Bulevar Louis Pasteur, Nº 35.Universidad de Málaga Málaga (SPAIN) {mavi,mdr,perez,conejo}@lcc.uma.es
More informationSpring 2007 Midterm Exam
15-381 Spring 2007 Midterm Exam Spring 2007 March 8 Name: Andrew ID: This is an open-book, open-notes examination. You have 80 minutes to complete this examination. Unless explicitly requested, we do not
More informationSupervised Learning with Neural Networks. We now look at how an agent might learn to solve a general problem by seeing examples.
Supervised Learning with Neural Networks We now look at how an agent might learn to solve a general problem by seeing examples. Aims: to present an outline of supervised learning as part of AI; to introduce
More informationDefending paid-peering on techno-economic grounds
Defending paid-peering on techno-economic grounds Constantine Dovrolis School of Computer Science Georgia Institute of Technology SDP workshop Minneapolis May 2018 1! Collaborators & funding sources Michael
More information6.033 Spring 2015 Lecture #11: Transport Layer Congestion Control Hari Balakrishnan Scribed by Qian Long
6.033 Spring 2015 Lecture #11: Transport Layer Congestion Control Hari Balakrishnan Scribed by Qian Long Please read Chapter 19 of the 6.02 book for background, especially on acknowledgments (ACKs), timers,
More informationThe Price of Selfishness in Network Coding
The Price of Selfishness in Network Coding Jason R. Marden and Michelle Effros Abstract We introduce a game theoretic framework for studying a restricted form of network coding in a general wireless network.
More informationFast Convergence of Regularized Learning in Games
Fast Convergence of Regularized Learning in Games Vasilis Syrgkanis Alekh Agarwal Haipeng Luo Robert Schapire Microsoft Research NYC Microsoft Research NYC Princeton University Microsoft Research NYC Strategic
More informationNet Neutrality and Inflation of Traffic
Introduction Net Neutrality and Inflation of Traffic Martin Peitz (MaCCI, University of Mannheim and CERRE) Florian Schuett (TILEC, CentER, Tilburg University) Symposium in Honor of Jean Tirole The Hague,
More informationDEGENERACY AND THE FUNDAMENTAL THEOREM
DEGENERACY AND THE FUNDAMENTAL THEOREM The Standard Simplex Method in Matrix Notation: we start with the standard form of the linear program in matrix notation: (SLP) m n we assume (SLP) is feasible, and
More informationSALSA: Super-Peer Assisted Live Streaming Architecture
SALSA: Super-Peer Assisted Live Streaming Architecture Jongtack Kim School of EECS, INMC Seoul National University Email: jkim@netlab.snu.ac.kr Yugyung Lee School of Computing and Engineering University
More informationA Self-Learning Repeated Game Framework for Optimizing Packet Forwarding Networks
A Self-Learning Repeated Game Framework for Optimizing Packet Forwarding Networks Zhu Han, Charles Pandana, and K.J. Ray Liu Department of Electrical and Computer Engineering, University of Maryland, College
More informationIntroduction to Algorithms / Algorithms I Lecturer: Michael Dinitz Topic: Algorithms and Game Theory Date: 12/3/15
600.363 Introduction to Algorithms / 600.463 Algorithms I Lecturer: Michael Dinitz Topic: Algorithms and Game Theory Date: 12/3/15 25.1 Introduction Today we re going to spend some time discussing game
More informationSimple and three-valued simple minimum coloring games
Math Meth Oper Res DOI 0.007/s0086-06-05- Simple and three-valued simple minimum coloring games M. Musegaas P. E. M. Borm M. Quant Received: 3 June 05 / Accepted: 0 April 06 The Author(s) 06. This article
More informationUsing Game Theory To Solve Network Security. A brief survey by Willie Cohen
Using Game Theory To Solve Network Security A brief survey by Willie Cohen Network Security Overview By default networks are very insecure There are a number of well known methods for securing a network
More informationTHE decentralized control architecture has been widely
234 IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 3, NO. 3, AUGUST 2007 Algorithms for Transitive Dependence-Based Coalition Formation Bo An, Zhiqi Shen, Chunyan Miao, and Daijie Cheng Abstract Coalition
More informationLeveraging Transitive Relations for Crowdsourced Joins*
Leveraging Transitive Relations for Crowdsourced Joins* Jiannan Wang #, Guoliang Li #, Tim Kraska, Michael J. Franklin, Jianhua Feng # # Department of Computer Science, Tsinghua University, Brown University,
More informationConflict Graphs for Parallel Stochastic Gradient Descent
Conflict Graphs for Parallel Stochastic Gradient Descent Darshan Thaker*, Guneet Singh Dhillon* Abstract We present various methods for inducing a conflict graph in order to effectively parallelize Pegasos.
More information!! What is virtual memory and when is it useful? !! What is demand paging? !! When should pages in memory be replaced?
Chapter 10: Virtual Memory Questions? CSCI [4 6] 730 Operating Systems Virtual Memory!! What is virtual memory and when is it useful?!! What is demand paging?!! When should pages in memory be replaced?!!
More informationAN ad-hoc network is a group of nodes without requiring
240 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 2, NO. 2, JUNE 2007 Securing Cooperative Ad-Hoc Networks Under Noise and Imperfect Monitoring: Strategies and Game Theoretic Analysis Wei
More informationStrategic Network Formation
Strategic Network Formation Sanjeev Goyal Cambridge University Plenary Talk GameNets 2009 Outline 1. Introduction: structure of networks 2. Strategic foundations 3. Unilateral linking Application: communication
More informationDepartments of Economics and Agricultural and Applied Economics Ph.D. Written Qualifying Examination August 2010 will not required
Departments of Economics and Agricultural and Applied Economics Ph.D. Written Qualifying Examination August 2010 Purpose All Ph.D. students are required to take the written Qualifying Examination. The
More informationLecture 2 - Introduction to Polytopes
Lecture 2 - Introduction to Polytopes Optimization and Approximation - ENS M1 Nicolas Bousquet 1 Reminder of Linear Algebra definitions Let x 1,..., x m be points in R n and λ 1,..., λ m be real numbers.
More informationPricing and Forwarding Games for Inter-domain Routing
Pricing and Forwarding Games for Inter-domain Routing Full version Ameya Hate, Elliot Anshelevich, Koushik Kar, and Michael Usher Department of Computer Science Department of Electrical & Computer Engineering
More informationBinary Relations McGraw-Hill Education
Binary Relations A binary relation R from a set A to a set B is a subset of A X B Example: Let A = {0,1,2} and B = {a,b} {(0, a), (0, b), (1,a), (2, b)} is a relation from A to B. We can also represent
More informationPage 129 Exercise 5: Suppose that the joint p.d.f. of two random variables X and Y is as follows: { c(x. 0 otherwise. ( 1 = c. = c
Stat Solutions for Homework Set Page 9 Exercise : Suppose that the joint p.d.f. of two random variables X and Y is as follows: { cx fx, y + y for y x, < x < otherwise. Determine a the value of the constant
More informationLecture 5 Finding meaningful clusters in data. 5.1 Kleinberg s axiomatic framework for clustering
CSE 291: Unsupervised learning Spring 2008 Lecture 5 Finding meaningful clusters in data So far we ve been in the vector quantization mindset, where we want to approximate a data set by a small number
More informationBasic Graph Theory with Applications to Economics
Basic Graph Theory with Applications to Economics Debasis Mishra February, 0 What is a Graph? Let N = {,..., n} be a finite set. Let E be a collection of ordered or unordered pairs of distinct elements
More informationThis article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION 1 Game Theoretic Approaches for Multiple Access in Wireless Networks: A Survey Khajonpong Akkarajitsakul, Ekram Hossain, Dusit Niyato,
More informationProblem set 2. Problem 1. Problem 2. Problem 3. CS261, Winter Instructor: Ashish Goel.
CS261, Winter 2017. Instructor: Ashish Goel. Problem set 2 Electronic submission to Gradescope due 11:59pm Thursday 2/16. Form a group of 2-3 students that is, submit one homework with all of your names.
More informationBroadcast in Ad hoc Wireless Networks with Selfish Nodes: A Bayesian Incentive Compatibility Approach
Broadcast in Ad hoc Wireless Networks with Selfish Nodes: A Bayesian Incentive Compatibility Approach N. Rama Suri Research Student, Electronic Enterprises Laboratory, Dept. of Computer Science and Automation,
More informationcoalition), by showing that if these are given, the problem becomes tractable in both cases. However, we then demonstrate that for a hybrid version of
Complexity of Determining Nonemptiness of the Core Λ Vincent Conitzer Tuomas Sandholm fconitzer, sandholmg@cs.cmu.edu Computer Science Department Carnegie Mellon University 5000 Forbes Avenue Pittsburgh,
More informationDatabase Management System Dr. S. Srinath Department of Computer Science & Engineering Indian Institute of Technology, Madras Lecture No.
Database Management System Dr. S. Srinath Department of Computer Science & Engineering Indian Institute of Technology, Madras Lecture No. # 3 Relational Model Hello everyone, we have been looking into
More information