Equitable Multi-Objective Optimization
|
|
- Emil Wiggins
- 5 years ago
- Views:
Transcription
1 Equitable Multi-Objective Optimization Krzysztof Rzadca Polish-Japanese Institute of Information Technology based on joint work with Denis Trystram, Adam Wierzbicki
2 In many situations, fairness is not equal division Cake gets bigger two halfs peel and juice [ oranges [Fisher, 98]
3 However, sometimes after an equal division the cake gets smaller. gini index higher -> less equal economic crisis most equal distribution 5.00 communism -> capitalism transition GDP per capita, $ (prices from 004) Income inequality vs GDP in Poland
4 Idea: extend multi-objective optimization to include fairness. globally-optimal solution fair solutions decreasing global efficiency Pareto front criteria minimalization
5 Table of Contents definition of multi-agent optimization axioms of equity equitable dominance by Generalized Lorentz Dominance one equitable solution: mapping & comparison all equitable solutions: algorithms & comparison
6 Multi-objective optimization problem with multiple agents that must be treated fairly. Centralized decision maker Agents' utilities depend on each other (shared system) Payoffs not transferable min (f(x), f(x),..., fn(x)) f(x) first agent's objective f(x) second agent's objective fn(x) last agent's objective Examples: multi-agent scheduling [Agnetis et al, 004] robust shortest path [Perny et al, 006] budget redistribution [Kostreva et al, 004] facility location [Marsch, 994]
7 (Values of) agents' utilities have to be directly comparable. fair division cardinal utilities finite goods to distribute each agent: max her share utility functions express strength of preferences utility utility B twice as good as A # received goods facility location [Marsch, 994] budget redistribution [Kostreva et al, 004] A B solutions robust shortest path [Perny et al, 006] multi-agent scheduling [Agnetis et al, 004]
8 economics and social science have similar problem: How to measure fairness of income distribution Sort outcomes from worst to best; measure cumulative outcome of n worst outcomes [wikipedia] Lorentz Curve [Lorentz 905]
9 Gini index expresses the unfairness in Lorentz curve. [Gini, 9] [wikipedia] gini index
10 economic crisis average salary ~ 0$/month end of first boom min salary ~ 00$/month [wikipedia] gini index: lower -> more equal Gini Index can favor inefficient solutions
11 Idea: compare equity of solutions that have the same global efficiency economics: Pigou-Dalton principle of transfers mathematics: majorization multi-agent minimization y = [y, y,..., y',..., y'',..., yn] y' > y'' (y' is worse) y + ε'' ε' preferred to y ε' = [0,...,0,...,ε,...,0,...0] ε''= [0,...,0,...,0,...,ε,...0] e.g. [9,6] is preferred to [0, 5] both [9,6] and [0,5] have the same global efficiency 5
12 Axiomatic theory of fairness: properties of a fair division work to be done 3 symmetry lazy workers (minimizing their work) number of hours: common valuation axioms: optimality principle of transfers
13 A fair solution is symmetric: no one is favored as fair 3 =as 3
14 A fair solution is optimal: it can't be improved unilaterally fairer 3 > than 3
15 Principle of transfers: Rob the riches, feed the poor fairer 3 > than 3
16 We define a relation of equitable dominance that fulfills these axioms Relation L : partial order on RN fulfils axioms of equity Which is more equitable: [4,6] or [0,]? [0, ] =L [, 0] (symmetry) [, 0] <L [4,8] (transfers) [4, 8] <L [4, 6] (Pareto-optimality) So, [0, ] less equitable than [4, 6]
17 These criteria can be encapsulated in a relation of Generalized Lorentz Dominance (3 agents minimizing outcomes) [Chong, 976] sort outcomes from the worst to the best [, 5, 3 ] -> [ 5, 3, ] [, 5, ] -> [ 5,, ] construct cumulative outcome vector: [worst outcome, sum of two worst outcomes,..., some of n worst outcomes] [5, 3, ] -> [ 5, 8, 9 ] [ 5,, ] -> [ 5, 7, 9] compare cumulative vectors by Pareto dominance [ 5, 7, 9] dominates [ 5, 8, 9 ]
18 Lorentz dominance gives us straightforward interpretation f(x) eq worse equitably equal equitably better pareto-better criteria minimization pareto-worse eq worse f(x)
19 f(x) The same results can be obtained by using axioms directly B types of dominance F E A D A[6,]=B[,6] C[00,]<[99,]<A[6,] D[7,0]<[6,]<[5,]<[4,3] < pareto < transfers < equitable C f(x) C<A (none is pareto-dominated by [6,]) A<E A[6,]<[4,4]<E[4,3] F[5,4]>[6,3] and A[6,]<[5,3]<[4,4] (no pareto-dominance)
20 Finding equitably-optimal solutions
21 Example application: scheduling problem with multiple agents [Agnetis et al., 004] One processor Two sets of jobs G ΣC i, ΣC 3 budget based approach: NP-hard i 5 7 red optimization goal: C green optimization goal: R CGi = = 5 R i t = = 6 Pareto-set can have exponential size
22 Multicriteria optimization can model fairness between mutliple users. C g i 3 C 3 =++3 (best total completion time) tg Ci =6 g i =4+5+6 Cgi = = (better for red agent) C g t i =3 Cgi = = 8
23 One Fair Solution
24 Ordered Weighted Average (OWA) with positive, strictly decreasing weights gives an equitable solution. [Ogryczak, 000] OWA [Yager, 988]: sort outcomes by increasing performance, then apply weighted average vector: [, 0, 5] weights: [0.5, 0., 0.] OWA=0.5* * * OWA(y') < OWA(y'') <=> y' equitably-dominates y'' sketch of proof for '<=' symmetry holds: OWA sorts outcomes optimality holds: one outcome decreased -> OWA decreased transfers holds: larger outcomes have larger weights
25 Other equitable aggregation functions are also possible. [Kostreva et al, 004] Aggregator function g(y) maps outcome vector to R min(g(f(x)) Requirements on g(y): strictly increasing (-> on each outcome) impartial (-> not sensitive to permutations of y) strictly Schur-convexity: examples: (s : R -> R, strictly convex, strictly monotonic) g(y) = Σs(yi) so, e.g. g(y) = Σ yik,k >
26 Classic fairness criteria give only one Best solution Σfi min max fi lexmin -> generalizes min max; -> OWA with infinite weight difference Σ-log fi -> ok, as strictly Schur convex Nash Bargaining Solution -> not compatible
27 Sum of criteria is too weak to produce an equitable solution. G R min (ΣC i + ΣC i ) = min ΣCi Minimized by Shortest Processing Time (SPT) schedule:... p p t This is unfair to red agent... Pairs of jobs have to be permutated... p p But should it be the only solution? t
28 min max can result in a very inefficient solution (...but lexmin is equitably optimal) min sum min max inefficiency
29 Nash Bargaining Solution takes into account best alternative to agreement. [Agnetis, 008] min ( g - f ) ( g - f) How to chose g? What is the best alternative? ( g, g )
30 All Equitable Solutions Pareto-prune k best sum
31 In the worst case, there are exponentially many equitablyoptimal solutions p p p+ p+ Red jobs delayed by - but last green jobs adds to green agents' goal: Thus, this schedule favours red by: p+ ( p+ - ) + p+ -3 After switching order of two jobs (i <= p): i red: + i i- green: - i- sum: + i- Generalized Lorentz Dominance: (xi == if there was a switch) [C Σxi i ; C + Σxi i] ( C < C, both are constants) Pareto-independent; thus all possible switches equitably-independent
32 Pareto-prune: Find the complete Pareto-optimal set, then remove equitably dominated solutions. possible problem: too many Pareto-optimal solutions
33 Applied to multi-agent scheduling: dynamic programming for Pareto-opt schedules Pareto-opt schedules with n jobs: extend Pareto-opt schedules with n- jobs remove Pareto-dominated combinations order between jobs of the same owner: SPT thus schedule specifies owners of the first n jobs
34 k-best sum: deteriorating min sum, find equitably-optimal solutions [Perny et al, 006]
35 Finding equitable schedule for the same total score find chains of jobs of the same length starting from the chain of longest job, greedy reduce the difference of payoffs Why it works? after each chain, the difference of payoffs is decreased by starting from the longest jobs, we are able to reduce errors
36 Finding next degradation in current schedule, for each pair of jobs: (longer after shorter) l m switch such pair compute total score: ΣCi+=(m-l) add to not visited schedules (heap by ΣCi) take the smallest element from heap m l
37 Bounding the number of steps [A, B] x) equitably f ( f(x) eq worse + [B,A] A criteria minimization = pareto-better x) equitably better f ( equal no equitable solutions here eq worse f(x)
38 Equitable multi-agent optimization: conclusions multi-agent optimization becomes important (shared system, centralized control) true multicriteria approach to fair optimization (many solutions to chose from) single equitable solution: generalization of some known concepts all equitable solutions: can be intractable... (->approximation algorithms?)
39 Equitable Multi-Objective Optimization Krzysztof Rzadca, Polish-Japanese Institute of Information Technology based on joint work with Denis Trystram, Adam Wierzbicki Thank you!
Multicriteria models for fair resource allocation 1
Control and Cybernetics vol. 36 (2007) No. 2 Multicriteria models for fair resource allocation 1 by W lodzimierz Ogryczak Warsaw University of Technology Institute of Control and Computation Engineering
More informationNetwork Dimensioning with Maximum Revenue Efficiency for the Fairness Index Grzegorz Zalewski 1 and Włodzimierz Ogryczak 2
Paper Network Dimensioning with Maximum Revenue Efficiency for the Fairness Index Grzegorz Zalewski 1 and Włodzimierz Ogryczak 2 1 National Institute of Telecommunications, Warsaw, Poland 2 Institute of
More informationAxiomatic bargaining. theory
Axiomatic bargaining theory Objective: To formulate and analyse reasonable criteria for dividing the gains or losses from a cooperative endeavour among several agents. We begin with a non-empty set of
More informationMultiple criteria linear programming model for portfolio selection
Annals of Operations Research 97 (2000) 143 162 143 Multiple criteria linear programming model for portfolio selection Włodzimierz Ogryczak Institute of Control and Computation Engineering, Warsaw University
More informationTHE REFERENCE POINT METHOD WITH LEXICOGRAPHIC MIN-ORDERING OF INDIVIDUAL ACHIEVEMENTS
Włodzimierz Ogryczak THE REFERENCE POINT METHOD WITH LEXICOGRAPHIC MIN-ORDERING OF INDIVIDUAL ACHIEVEMENTS INTRODUCTION Typical multiple criteria optimization methods aggregate the individual outcomes
More informationInequality measures and equitable approaches to location problems q
European Journal of Operational Research 122 (2000) 374±391 www.elsevier.com/locate/orms Inequality measures and equitable approaches to location problems q Wøodzimierz Ogryczak * Institute of Informatics,
More informationInfinite order Lorenz dominance for fair multiagent optimization
Infinite order Lorenz dominance for fair multiagent optimization ABSTRACT Boris Golden LIX Ecole polytechnique 91128 Palaiseau Cedex, France boris.golden@polytechnique.edu This paper deals with fair assignment
More informationHousehold Heterogeneity and Inequality Measurement
Household Heterogeneity and Inequality Measurement Alain Trannoy EHESS, Greqam-Idep, Marseille 4 th Canazei Winter School 1 Three allocation problems To cope with the problems raised by the fact that the
More informationOWA-based Search in State Space Graphs with Multiple Cost Functions
OWA-based Search in State Space Graphs with Multiple Cost Functions Lucie Galand LIP6 - University of Paris VI 4 Place Jussieu 75252 Paris Cedex 05, France lucie.galand@lip6.fr Olivier Spanjaard LIP6 -
More informationNo-envy in Queueing Problems
No-envy in Queueing Problems Youngsub Chun School of Economics Seoul National University Seoul 151-742, Korea and Department of Economics University of Rochester Rochester, NY 14627, USA E-mail: ychun@plaza.snu.ac.kr
More informationRelative Benefit Equilibrating Bargaining Solution and the Ordinal Interpretation of Gauthier s Arbitration Scheme
Relative Benefit Equilibrating Bargaining Solution and the Ordinal Interpretation of Gauthier s Arbitration Scheme Mantas Radzvilas July 2017 Abstract In 1986 David Gauthier proposed an arbitration scheme
More informationarxiv: v2 [cs.ds] 27 Nov 2014
Single machine scheduling problems with uncertain parameters and the OWA criterion arxiv:1405.5371v2 [cs.ds] 27 Nov 2014 Adam Kasperski Institute of Industrial Engineering and Management, Wroc law University
More informationAGGREGATION OPERATORS FOR MULTICRITERIA DECISION AID. Jean-Luc Marichal University of Liège
AGGREGATION OPERATORS FOR MULTICRITERIA DECISION AID by Jean-Luc Marichal University of Liège 1 2 1. Aggregation in MCDM Set of alternatives A = {a, b, c,...} Set of criteria N = {1,..., n}. For all i
More informationCS 598RM: Algorithmic Game Theory, Spring Practice Exam Solutions
CS 598RM: Algorithmic Game Theory, Spring 2017 1. Answer the following. Practice Exam Solutions Agents 1 and 2 are bargaining over how to split a dollar. Each agent simultaneously demands share he would
More informationEquality Measures Properties for Location Problems
Equality Measures Properties for Location Problems Maria Barbati Carmela Piccolo October 16, 2015 Abstract The objectives underlying location decisions can be various. Among them, equity objectives have
More informationSequencing problems with uncertain parameters and the OWA criterion
Sequencing problems with uncertain parameters and the OWA criterion Adam Kasperski 1 Paweł Zieliński 2 1 Institute of Industrial Engineering and Management Wrocław University of Technology, POLAND 2 Institute
More informationThis corresponds to a within-subject experiment: see same subject make choices from different menus.
Testing Revealed Preference Theory, I: Methodology The revealed preference theory developed last time applied to a single agent. This corresponds to a within-subject experiment: see same subject make choices
More informationWłodzimierz Ogryczak. Warsaw University of Technology, ICCE ON ROBUST SOLUTIONS TO MULTI-OBJECTIVE LINEAR PROGRAMS. Introduction. Abstract.
Włodzimierz Ogryczak Warsaw University of Technology, ICCE ON ROBUST SOLUTIONS TO MULTI-OBJECTIVE LINEAR PROGRAMS Abstract In multiple criteria linear programming (MOLP) any efficient solution can be found
More informationMicroeconomics. Joana Pais. Fall Joana Pais
Microeconomics Fall 2016 Primitive notions There are four building blocks in any model of consumer choice. They are the consumption set, the feasible set, the preference relation, and the behavioural assumption.
More informationWorst-Case Efficiency Analysis of Queueing Disciplines
Worst-Case Efficiency Analysis of Queueing Disciplines Damon Mosk-Aoyama and Tim Roughgarden Department of Computer Science, Stanford University, 353 Serra Mall, Stanford, CA 94305 Introduction Consider
More informationNash Bargaining in Ordinal Environments
Nash Bargaining in Ordinal Environments By Özgür Kıbrıs April 19, 2012 Abstract We analyze the implications of Nash s (1950) axioms in ordinal bargaining environments; there, the scale invariance axiom
More informationThe measurement of welfare change
The measurement of welfare change Walter Bossert Department of Economics and CIREQ, University of Montreal walter.bossert@videotron.ca Bhaskar Dutta Department of Economics, University of Warwick B.Dutta@warwick.ac.uk
More informationPotential Games. Krzysztof R. Apt. CWI, Amsterdam, the Netherlands, University of Amsterdam. Potential Games p. 1/3
Potential Games p. 1/3 Potential Games Krzysztof R. Apt CWI, Amsterdam, the Netherlands, University of Amsterdam Potential Games p. 2/3 Overview Best response dynamics. Potential games. Congestion games.
More informationThe Interdisciplinary Center, Herzliya School of Economics Advanced Microeconomics Fall Bargaining The Axiomatic Approach
The Interdisciplinary Center, Herzliya School of Economics Advanced Microeconomics Fall 2011 Bargaining The Axiomatic Approach Bargaining problem Nash s (1950) work is the starting point for formal bargaining
More informationFairness Criteria for Fair Division of Indivisible Goods
Sylvain Bouveret LIG (STeamer) Ensimag / Grenoble INP Michel Lemaître Formerly Onera Toulouse Séminaire de l équipe ROSP du laboratoire G-SCOP Grenoble, March 24, 2016 Introduction A fair division problem...
More informationCS 781 Lecture 9 March 10, 2011 Topics: Local Search and Optimization Metropolis Algorithm Greedy Optimization Hopfield Networks Max Cut Problem Nash
CS 781 Lecture 9 March 10, 2011 Topics: Local Search and Optimization Metropolis Algorithm Greedy Optimization Hopfield Networks Max Cut Problem Nash Equilibrium Price of Stability Coping With NP-Hardness
More informationMulti-agent scheduling problems
Multi-agent scheduling problems Alessandro Agnetis, Università di Siena Dipartimento di Ingegneria dell Informazione Toulouse, LAAS-CNRS 13/5/2011 INTRODUCTION: MULTI-AGENT SCHEDULING Centralized decision
More informationApproximation Algorithms (Load Balancing)
July 6, 204 Problem Definition : We are given a set of n jobs {J, J 2,..., J n }. Each job J i has a processing time t i 0. We are given m identical machines. Problem Definition : We are given a set of
More information1 Surplus Division. 2 Fair Distribution (Moulin 03) 2.1 Four Principles of Distributive Justice. Output (surplus) to be divided among several agents.
1 Surplus Division 2 Fair Distribution (Moulin 03) Output (surplus) to be divided among several agents. Issues: How to divide? How to produce? How to organize? Plus: adverse selection, moral hazard,...
More informationEcon 2148, spring 2019 Statistical decision theory
Econ 2148, spring 2019 Statistical decision theory Maximilian Kasy Department of Economics, Harvard University 1 / 53 Takeaways for this part of class 1. A general framework to think about what makes a
More informationBargaining, Contracts, and Theories of the Firm. Dr. Margaret Meyer Nuffield College
Bargaining, Contracts, and Theories of the Firm Dr. Margaret Meyer Nuffield College 2015 Course Overview 1. Bargaining 2. Hidden information and self-selection Optimal contracting with hidden information
More informationComment on The Veil of Public Ignorance
Comment on The Veil of Public Ignorance Geoffroy de Clippel February 2010 Nehring (2004) proposes an interesting methodology to extend the utilitarian criterion defined under complete information to an
More informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2016
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2016 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationRedistribution Mechanisms for Assignment of Heterogeneous Objects
Redistribution Mechanisms for Assignment of Heterogeneous Objects Sujit Gujar Dept of Computer Science and Automation Indian Institute of Science Bangalore, India sujit@csa.iisc.ernet.in Y Narahari Dept
More informationarxiv: v1 [cs.ds] 17 Jul 2013
Bottleneck combinatorial optimization problems with uncertain costs and the OWA criterion arxiv:137.4521v1 [cs.ds] 17 Jul 213 Adam Kasperski Institute of Industrial Engineering and Management, Wroc law
More informationGame Theory: introduction and applications to computer networks
Game Theory: introduction and applications to computer networks Introduction Giovanni Neglia INRIA EPI Maestro 27 January 2014 Part of the slides are based on a previous course with D. Figueiredo (UFRJ)
More informationHypothetical Bargaining and Equilibrium Refinement in Non-Cooperative Games
Hypothetical Bargaining and Equilibrium Refinement in Non-Cooperative Games Mantas Radzvilas December 2016 Abstract Virtual bargaining theory suggests that social agents aim to resolve non-cooperative
More informationPublic Economics Ben Heijdra Chapter 9: Introduction to Normative Public Economics
Public Economics: Chapter 9 1 Public Economics Ben Heijdra Chapter 9: Introduction to Normative Public Economics Objectives of this chapter Public Economics: Chapter 9 2 Read Atkinson & Stiglitz (1980,
More informationFair Public Decision Making
1 Fair Public Decision Making VINCENT CONITZER, Duke University RUPERT FREEMAN, Duke University NISARG SHAH, Harvard University We generalize the classic problem of fairly allocating indivisible goods
More informationarxiv: v2 [cs.dm] 2 Mar 2017
Shared multi-processor scheduling arxiv:607.060v [cs.dm] Mar 07 Dariusz Dereniowski Faculty of Electronics, Telecommunications and Informatics, Gdańsk University of Technology, Gdańsk, Poland Abstract
More informationEfficiency, Fairness and Competitiveness in Nash Bargaining Games
Efficiency, Fairness and Competitiveness in Nash Bargaining Games Deeparnab Chakrabarty, Gagan Goel 2, Vijay V. Vazirani 2, Lei Wang 2 and Changyuan Yu 3 Department of Combinatorics and Optimization, University
More informationConsistent multidimensional poverty comparisons
Preliminary version - Please do not distribute Consistent multidimensional poverty comparisons Kristof Bosmans a Luc Lauwers b Erwin Ooghe b a Department of Economics, Maastricht University, Tongersestraat
More informationEconomic Core, Fair Allocations, and Social Choice Theory
Chapter 9 Nathan Smooha Economic Core, Fair Allocations, and Social Choice Theory 9.1 Introduction In this chapter, we briefly discuss some topics in the framework of general equilibrium theory, namely
More informationEconomics 201B Economic Theory (Spring 2017) Bargaining. Topics: the axiomatic approach (OR 15) and the strategic approach (OR 7).
Economics 201B Economic Theory (Spring 2017) Bargaining Topics: the axiomatic approach (OR 15) and the strategic approach (OR 7). The axiomatic approach (OR 15) Nash s (1950) work is the starting point
More informationCooperative Games. M2 ISI Systèmes MultiAgents. Stéphane Airiau LAMSADE
Cooperative Games M2 ISI 2015 2016 Systèmes MultiAgents Stéphane Airiau LAMSADE M2 ISI 2015 2016 Systèmes MultiAgents (Stéphane Airiau) Cooperative Games 1 Why study coalitional games? Cooperative games
More informationSURPLUS SHARING WITH A TWO-STAGE MECHANISM. By Todd R. Kaplan and David Wettstein 1. Ben-Gurion University of the Negev, Israel. 1.
INTERNATIONAL ECONOMIC REVIEW Vol. 41, No. 2, May 2000 SURPLUS SHARING WITH A TWO-STAGE MECHANISM By Todd R. Kaplan and David Wettstein 1 Ben-Gurion University of the Negev, Israel In this article we consider
More informationStrategic Properties of Heterogeneous Serial Cost Sharing
Strategic Properties of Heterogeneous Serial Cost Sharing Eric J. Friedman Department of Economics, Rutgers University New Brunswick, NJ 08903. January 27, 2000 Abstract We show that serial cost sharing
More informationUC Berkeley Haas School of Business Game Theory (EMBA 296 & EWMBA 211) Summer Social learning and bargaining (axiomatic approach)
UC Berkeley Haas School of Business Game Theory (EMBA 296 & EWMBA 211) Summer 2015 Social learning and bargaining (axiomatic approach) Block 4 Jul 31 and Aug 1, 2015 Auction results Herd behavior and
More information( )! ±" and g( x)! ±" ], or ( )! 0 ] as x! c, x! c, x! c, or x! ±". If f!(x) g!(x) "!,
IV. MORE CALCULUS There are some miscellaneous calculus topics to cover today. Though limits have come up a couple of times, I assumed prior knowledge, or at least that the idea makes sense. Limits are
More informationA FAIR SOLUTION TO THE COMPENSATION PROBLEM. Giacomo Valletta WORK IN PROGRESS, PLEASE DO NOT QUOTE. Introduction
A FAIR SOLUTION TO THE COMPENSATION PROBLEM Giacomo Valletta WORK IN PROGRESS, PLEASE DO NOT QUOTE Abstract. In this paper we deal with a fair division model concerning compensation among individuals endowed
More informationExact algorithms for OWA-optimization in multiobjective spanning tree problems
Exact algorithms for OWA-optimization in multiobjective spanning tree problems Lucie Galand,a, Olivier Spanjaard b a LAMSADE-CNRS, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, F-75775
More informationContracts under Asymmetric Information
Contracts under Asymmetric Information 1 I Aristotle, economy (oiko and nemo) and the idea of exchange values, subsequently adapted by Ricardo and Marx. Classical economists. An economy consists of a set
More informationSelfish Multi-User Task Scheduling
Selfish Multi-User Task Scheduling Thomas E. Carroll and Daniel Grosu Dept. of Computer Science Wayne State University 5143 Cass Avenue Detroit, Michigan 48202 USA Email: {tec, dgrosu}@cs.wayne.edu Abstract
More informationBackground notes on bargaining
ackground notes on bargaining Cooperative bargaining - bargaining theory related to game theory - nice book is Muthoo (1999) argaining theory with applications; - also, Dixit and Skeath's game theory text
More informationBargaining Efficiency and the Repeated Prisoners Dilemma. Bhaskar Chakravorti* and John Conley**
Bargaining Efficiency and the Repeated Prisoners Dilemma Bhaskar Chakravorti* and John Conley** Published as: Bhaskar Chakravorti and John P. Conley (2004) Bargaining Efficiency and the repeated Prisoners
More informationWeek 6: Consumer Theory Part 1 (Jehle and Reny, Chapter 1)
Week 6: Consumer Theory Part 1 (Jehle and Reny, Chapter 1) Tsun-Feng Chiang* *School of Economics, Henan University, Kaifeng, China November 2, 2014 1 / 28 Primitive Notions 1.1 Primitive Notions Consumer
More informationMicroeconomic Algorithms for Flow Control in Virtual Circuit Networks (Subset in Infocom 1989)
Microeconomic Algorithms for Flow Control in Virtual Circuit Networks (Subset in Infocom 1989) September 13th, 1995 Donald Ferguson*,** Christos Nikolaou* Yechiam Yemini** *IBM T.J. Watson Research Center
More informationChoice under Uncertainty
In the Name of God Sharif University of Technology Graduate School of Management and Economics Microeconomics 2 44706 (1394-95 2 nd term) Group 2 Dr. S. Farshad Fatemi Chapter 6: Choice under Uncertainty
More informationBeyond average and minimax in MILP
Beyond average and minimax in MILP [source file: MinMaxBeta-MILP COR-5.tex] Carlo Filippi W lodzimierz Ogryczak M. Grazia Speranza Abstract Mixed-Integer Linear Programming (MILP) models often optimize
More informationMeta-Heuristic Approach to Proportional Fairness
Evolutionary Intelligence manuscript No. (will be inserted by the editor) Meta-Heuristic Approach to Proportional Fairness Mario Köppen Kaori Yoshida Kei Ohnishi Masato Tsuru Received: date / Accepted:
More informationPresentation for CSG399 By Jian Wen
Presentation for CSG399 By Jian Wen Outline Skyline Definition and properties Related problems Progressive Algorithms Analysis SFS Analysis Algorithm Cost Estimate Epsilon Skyline(overview and idea) Skyline
More informationwhere u is the decision-maker s payoff function over her actions and S is the set of her feasible actions.
Seminars on Mathematics for Economics and Finance Topic 3: Optimization - interior optima 1 Session: 11-12 Aug 2015 (Thu/Fri) 10:00am 1:00pm I. Optimization: introduction Decision-makers (e.g. consumers,
More informationPoverty measures and poverty orderings
Statistics & Operations Research Transactions SORT 31 2) July-December 27, 169-18 ISSN: 1696-2281 www.idescat.net/sort Statistics & Operations Research c Institut d Estadística de Transactions Catalunya
More informationDynamic Fairness: Mobility, Inequality, and the Distribution of Prospects
Dynamic Fairness: Mobility, Inequality, and the Distribution of Prospects Baochun Peng 1 The Hong Kong Polytechnic University Haidong Yuan The Chinese University of Hong Kong Abstract This paper clarifies
More informationDynamic Fairness: Mobility, Inequality, and the Distribution of Prospects
Dynamic Fairness: Mobility, Inequality, and the Distribution of Prospects Baochun Peng 1 The Hong Kong Polytechnic University Haidong Yuan The Chinese University of Hong Kong Abstract This paper clarifies
More informationGame Theory. Bargaining Theory. ordi Massó. International Doctorate in Economic Analysis (IDEA) Universitat Autònoma de Barcelona (UAB)
Game Theory Bargaining Theory J International Doctorate in Economic Analysis (IDEA) Universitat Autònoma de Barcelona (UAB) (International Game Theory: Doctorate Bargainingin Theory Economic Analysis (IDEA)
More informationTrade, Inequality and Costly Redistribution
Trade, Inequality and Costly Redistribution Pol Antràs Alonso de Gortari Oleg Itskhoki Harvard Harvard Princeton ILO Symposium September 2015 1 / 30 Introduction International trade raises real income
More informationThe price of anarchy of finite congestion games
The price of anarchy of finite congestion games George Christodoulou Elias Koutsoupias Abstract We consider the price of anarchy of pure Nash equilibria in congestion games with linear latency functions.
More informationCombinatorial Agency of Threshold Functions
Combinatorial Agency of Threshold Functions Shaili Jain 1 and David C. Parkes 2 1 Yale University, New Haven, CT shaili.jain@yale.edu 2 Harvard University, Cambridge, MA parkes@eecs.harvard.edu Abstract.
More informationSecond Welfare Theorem
Second Welfare Theorem Econ 2100 Fall 2015 Lecture 18, November 2 Outline 1 Second Welfare Theorem From Last Class We want to state a prove a theorem that says that any Pareto optimal allocation is (part
More informationCooperative bargaining: independence and monotonicity imply disagreement
Cooperative bargaining: independence and monotonicity imply disagreement Shiran Rachmilevitch September 23, 2012 Abstract A unique bargaining solution satisfies restricted monotonicity, independence of
More informationPMS 2012 April Leuven
The multiagent project scheduling problem: complexity of finding a minimum-makespan Nash equilibrium C. Briand A. Agnetis and J.-C Billaut (briand@laas.fr, agnetis@dii.unisi.it, billaut@univ-tours.fr)
More informationMS&E 246: Lecture 18 Network routing. Ramesh Johari
MS&E 246: Lecture 18 Network routing Ramesh Johari Network routing Last lecture: a model where N is finite Now: assume N is very large Formally: Represent the set of users as a continuous interval, [0,
More informationSequential Algorithms for Exact and Approximate Max-Min Fair Bandwidth Allocation
Sequential Algorithms for Exact and Approximate Max-Min Fair Bandwidth Allocation Włodzimierz Ogryczak Institute of Control & Computation Engineering Warsaw University of Technology 00 665 Warsaw, Poland
More informationConsumer theory Topics in consumer theory. Microeconomics. Joana Pais. Fall Joana Pais
Microeconomics Fall 2016 Indirect utility and expenditure Properties of consumer demand The indirect utility function The relationship among prices, incomes, and the maximised value of utility can be summarised
More informationFirst Welfare Theorem
First Welfare Theorem Econ 2100 Fall 2017 Lecture 17, October 31 Outline 1 First Welfare Theorem 2 Preliminaries to Second Welfare Theorem Past Definitions A feasible allocation (ˆx, ŷ) is Pareto optimal
More informationPRESENTATION ON THE TOPIC ON INEQUALITY COMPARISONS PRESENTED BY MAG.SYED ZAFAR SAEED
PRESENTATION ON THE TOPIC ON INEQUALITY COMPARISONS PRESENTED BY MAG.SYED ZAFAR SAEED Throughout this paper, I shall talk in terms of income distributions among families. There are two points of contention.
More informationOnline Packet Routing on Linear Arrays and Rings
Proc. 28th ICALP, LNCS 2076, pp. 773-784, 2001 Online Packet Routing on Linear Arrays and Rings Jessen T. Havill Department of Mathematics and Computer Science Denison University Granville, OH 43023 USA
More informationCO759: Algorithmic Game Theory Spring 2015
CO759: Algorithmic Game Theory Spring 2015 Instructor: Chaitanya Swamy Assignment 1 Due: By Jun 25, 2015 You may use anything proved in class directly. I will maintain a FAQ about the assignment on the
More informationTwo Desirable Fairness Concepts for Allocation of Indivisible Objects under Ordinal Preferences
Two Desirable Fairness Concepts for Allocation of Indivisible Objects under Ordinal Preferences HARIS AZIZ and SERGE GASPERS and SIMON MACKENZIE and TOBY WALSH Data61 and UNSW Fair allocation of indivisible
More informationFollow links for Class Use and other Permissions. For more information send to:
COPYRIGHT NOTICE: Ariel Rubinstein: Lecture Notes in Microeconomic Theory is published by Princeton University Press and copyrighted, c 2006, by Princeton University Press. All rights reserved. No part
More informationA Truthful Mechanism for Fair Load Balancing in Distributed Systems Λ
A Truthful Mechanism for Fair Load Balancing in Distributed Systems Λ Daniel Grosu and Anthony T. Chronopoulos Department of Computer Science, University of Texas at San Antonio, 6900 N. Loop 1604 West,
More informationNegative Income Taxes, Inequality and Poverty
Negative Income Taxes, Inequality and Poverty Constantine Angyridis Brennan S. Thompson Department of Economics Ryerson University July 8, 2011 Overview We use a dynamic heterogeneous agents general equilibrium
More informationECS122A Handout on NP-Completeness March 12, 2018
ECS122A Handout on NP-Completeness March 12, 2018 Contents: I. Introduction II. P and NP III. NP-complete IV. How to prove a problem is NP-complete V. How to solve a NP-complete problem: approximate algorithms
More informationResource Allocation via the Median Rule: Theory and Simulations in the Discrete Case
Resource Allocation via the Median Rule: Theory and Simulations in the Discrete Case Klaus Nehring Clemens Puppe January 2017 **** Preliminary Version ***** Not to be quoted without permission from the
More informationExamples. 1.1 Cones in Vector Spaces
Examples. Cones in Vector Spaces Vector optimization in partially ordered spaces requires, among other things, that one studies properties of cones; as arguments recall: Conic approximation of sets, e.g.,
More informationEquity in Production Economies with Dedicated Factors. Laurence Kranich Department of Economics University at Albany
Equity in Production Economies with Dedicated Factors Laurence Kranich Department of Economics University at Albany September 6, 2017 Abstract In this paper I consider the problem of determining an equitable
More informationPERCOLATION IN SELFISH SOCIAL NETWORKS
PERCOLATION IN SELFISH SOCIAL NETWORKS Charles Bordenave UC Berkeley joint work with David Aldous (UC Berkeley) PARADIGM OF SOCIAL NETWORKS OBJECTIVE - Understand better the dynamics of social behaviors
More informationAN ORDINAL SOLUTION TO BARGAINING PROBLEMS WITH MANY PLAYERS
AN ORDINAL SOLUTION TO BARGAINING PROBLEMS WITH MANY PLAYERS ZVI SAFRA AND DOV SAMET Abstract. Shapley proved the existence of an ordinal, symmetric and efficient solution for three-player bargaining problems.
More informationhal , version 1-27 Mar 2014
Author manuscript, published in "2nd Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2005), New York, NY. : United States (2005)" 2 More formally, we denote by
More informationEnergy-efficient scheduling
Energy-efficient scheduling Guillaume Aupy 1, Anne Benoit 1,2, Paul Renaud-Goud 1 and Yves Robert 1,2,3 1. Ecole Normale Supérieure de Lyon, France 2. Institut Universitaire de France 3. University of
More informationA Constructive Proof of the Nash Bargaining Solution
Working Paper 14/0 /01 A Constructive Proof of the Nash Bargaining Solution Luís Carvalho ISCTE - Instituto Universitário de Lisboa BRU-IUL Unide-IUL) Av. Forças Armadas 1649-126 Lisbon-Portugal http://bru-unide.iscte.pt/
More informationCompetitive Equilibrium
Competitive Equilibrium Econ 2100 Fall 2017 Lecture 16, October 26 Outline 1 Pareto Effi ciency 2 The Core 3 Planner s Problem(s) 4 Competitive (Walrasian) Equilibrium Decentralized vs. Centralized Economic
More informationTHE IMPACT ON SCALING ON THE PAIR-WISE COMPARISON OF THE ANALYTIC HIERARCHY PROCESS
ISAHP 200, Berne, Switzerland, August 2-4, 200 THE IMPACT ON SCALING ON THE PAIR-WISE COMPARISON OF THE ANALYTIC HIERARCHY PROCESS Yuji Sato Department of Policy Science, Matsusaka University 846, Kubo,
More informationMS&E 246: Lecture 17 Network routing. Ramesh Johari
MS&E 246: Lecture 17 Network routing Ramesh Johari Network routing Basic definitions Wardrop equilibrium Braess paradox Implications Network routing N users travel across a network Transportation Internet
More informationEfficiency and Braess Paradox under Pricing
Efficiency and Braess Paradox under Pricing Asuman Ozdaglar Joint work with Xin Huang, [EECS, MIT], Daron Acemoglu [Economics, MIT] October, 2004 Electrical Engineering and Computer Science Dept. Massachusetts
More informationPiercing the Veil of Ignorance
Piercing the Veil of Ignorance Shachar Kariv UC Berkeley William R. Zame UCLA September 15, 2008 Abstract Theories of justice in the spirit of Harsanyi and Rawls argue that fair-minded people should aspire
More informationIntroduction to Formal Epistemology Lecture 5
Introduction to Formal Epistemology Lecture 5 Eric Pacuit and Rohit Parikh August 17, 2007 Eric Pacuit and Rohit Parikh: Introduction to Formal Epistemology, Lecture 5 1 Plan for the Course Introduction,
More informationThe Adjusted Winner Procedure : Characterizations and Equilibria
The Adjusted Winner Procedure : Characterizations and Equilibria Simina Brânzei Aarhus University, Denmark Joint with Haris Aziz, Aris Filos-Ratsikas, and Søren Frederiksen Background Adjusted Winner:
More informationGeneral Equilibrium. General Equilibrium, Berardino. Cesi, MSc Tor Vergata
General Equilibrium Equilibrium in Consumption GE begins (1/3) 2-Individual/ 2-good Exchange economy (No production, no transaction costs, full information..) Endowment (Nature): e Private property/ NO
More information