Potential games are necessary to ensure pure Nash equilibria in cost sharing games.

Slides:

Advertisements

Similar presentations

Presenter Name(s) Issue date National Student.

Advertisements

Section B Managerial and individual decision problems 1. Externalities and regulation Applications and case studies: pollution control, health care, education,

Minimizing Efficiency Loss in Mechanism and Protocol Design Tim Roughgarden (Stanford) includes joint work with: Shuchi Chawla (Wisconsin), Ho-Lin Chen.

Best Response Dynamics in Multicast Cost Sharing

Dispatching to Incentivize Fast Service in Multi-Server Queues Raga Gopalakrishnan and Adam Wierman California Institute of Technology Sherwin Doroudi.

Performance and Strategy in Competitive Markets Chapter 8.

Inefficiency of equilibria, and potential games Computational game theory Spring 2008 Michal Feldman TexPoint fonts used in EMF. Read the TexPoint manual.

Conditional Equilibrium Outcomes via Ascending Price Processes Joint work with Hu Fu and Robert Kleinberg (Computer Science, Cornell University) Ron Lavi.

1 Approximation in Algorithmic Game Theory Robust Approximation Bounds for Equilibria and Auctions Tim Roughgarden Stanford University.

1 Robust Price of Anarchy Bounds via Smoothness Arguments Tim Roughgarden Stanford University.

County-level Estimates of Diagnosed Diabetes Incidence among Adults aged ≥ 20 years old Trends

Network Security: an Economic Perspective Marc Lelarge (INRIA-ENS) currently visiting STANFORD TRUST seminar, Berkeley 2011.

Source: Financial Times of London Global Banks 1999 – 2009 “Changing of the Guard”

Risk Models and Controlled Mitigation of IT Security R. Ann Miura-Ko Stanford University February 27, 2009.

Name ____________________ Date ___________ Period ____.

An Architectural View of Game Theoretic Control Raga Gopalakrishnan and Adam Wierman California Institute of Technology Jason R. Marden University of Colorado.

County-level Estimates of Diagnosed Diabetes among Adults aged ≥ 20 years: United States 2004

Characterizing distribution rules for cost sharing games Raga Gopalakrishnan Caltech Joint work with Jason R. Marden & Adam Wierman.

Price of Stability Li Jian Fudan University May, 8 th,2007 Introduction to.

(CS/SS 241) Introduction to SISL: Topics in Algorithmic game theory Adam Wierman – 258 Jorgensen John Ledyard – 102 Baxter Jason R. Marden – 335 Moore.

A Prior-Free Revenue Maximizing Auction for Secondary Spectrum Access Ajay Gopinathan and Zongpeng Li IEEE INFOCOM 2011, Shanghai, China.

Regret Minimization and the Price of Total Anarchy Paper by A. Blum, M. Hajiaghayi, K. Ligett, A.Roth Presented by Michael Wunder.

1 Smooth Games and Intrinsic Robustness Christodoulou and Koutsoupias, Roughgarden Slides stolen/modified from Tim Roughgarden TexPoint fonts used in EMF.

Xujin Chen, Xiaodong Hu Institute of Applied Mathematics Chinese Academy of Sciences Network Routing Games on Ring Infrastructure G CN-GER Conf on Math.

1 Algorithmic Game Theoretic Perspectives in Networking Dr. Liane Lewin-Eytan.

Algorithmic and Economic Aspects of Networks Nicole Immorlica.

Xu Chen Xiaowen Gong Lei Yang Junshan Zhang

CRESCCO Project IST Work Package 2 Algorithms for Selfish Agents V. Auletta, P. Penna and G. Persiano Università di Salerno

Beyond selfish routing: Network Formation Games. Network Formation Games NFGs model the various ways in which selfish agents might create/use networks.

Autonomous Target Assignment: A Game Theoretical Formulation Gurdal Arslan & Jeff Shamma Mechanical and Aerospace Engineering UCLA AFOSR / MURI.

1 On the price of anarchy and stability of correlated equilibria of linear congestion games By George Christodoulou Elias Koutsoupias Presented by Efrat.

The Price Of Stability for Network Design with Fair Cost Allocation Elliot Anshelevich, Anirban Dasgupta, Jon Kleinberg, Eva Tardos, Tom Wexler, Tim Roughgarden.

How Bad is Selfish Routing? Tim Roughgarden & Eva Tardos Presented by Wonhong Nam

Near Optimal Network Design With Selfish Agents Eliot Anshelevich Anirban Dasupta Eva Tardos Tom Wexler Presented by: Andrey Stolyarenko School of CS,

Potential games, Congestion games Computational game theory Spring 2010 Adapting slides by Michal Feldman TexPoint fonts used in EMF. Read the TexPoint.

Algorithms, Games and the Internet Christos H. Papadimitriou UC Berkeley

Network Formation Games. Netwok Formation Games NFGs model distinct ways in which selfish agents might create and evaluate networks We’ll see two models:

How Bad is Selfish Routing A survey on existing models for selfish routing Professor John Lui, David Yau and Dah-Ming Qiu presented by Joe W.J. Jiang

Network Formation Games. Netwok Formation Games NFGs model distinct ways in which selfish agents might create and evaluate networks We’ll see two models:

Price of Anarchy Bounds Price of Anarchy Convergence Based on Slides by Amir Epstein and by Svetlana Olonetsky Modified/Corrupted by Michal Feldman and.

1 Issues on the border of economics and computation נושאים בגבול כלכלה וחישוב Congestion Games, Potential Games and Price of Anarchy Liad Blumrosen ©

Uniform Price Auctions: Equilibria and Efficiency Vangelis Markakis Athens University of Economics & Business (AUEB) 1 Orestis Telelis University of Liverpool.

Raga Gopalakrishnan University of Colorado at Boulder Sean D. Nixon (University of Vermont) Jason R. Marden (University of Colorado at Boulder) Stable.

Mechanisms for Making Crowds Truthful Andrew Mao, Sergiy Nesterko.

A Study of Central Auction Based Wholesale Electricity Markets S. Ceppi and N. Gatti.

Price of Anarchy Georgios Piliouras. Games (i.e. Multi-Body Interactions) Interacting entities Pursuing their own goals Lack of centralized control Prediction?

Network Congestion Games

Beyond selfish routing: Network Games. Network Games NGs model the various ways in which selfish agents strategically interact in using a network They.

Beyond selfish routing: Network Games. Network Games NGs model the various ways in which selfish users (i.e., players) strategically interact in using.

Designing Games for Distributed Optimization Na Li and Jason R. Marden IEEE Journal of Selected Topics in Signal Processing, Vol. 7, No. 2, pp ,

Vasilis Syrgkanis Cornell University

The Price of Routing Unsplittable Flow Yossi Azar Joint work with B. Awerbuch and A. Epstein.

Network Formation Games. NFGs model distinct ways in which selfish agents might create and evaluate networks We’ll see two models: Global Connection Game.

Instructor: Ruta Mehta TA: Omkar Thakoor

L23 Public Goods.

Instructor: Ruta Mehta TA: TBA

Christos H. Papadimitriou UC Berkeley

Éva Tardos Cornell University

L24 Public Goods.

L24 Public Goods.

L23 Public Goods.

L24 Public Goods.

Algorithmic Problems Related To The Internet

Oliver Schulte Petra Berenbrink Simon Fraser University

L24 Public Goods.

The Price of Routing Unsplittable Flow

Network Formation Games

L24 Public Goods.

Richard Ma, Sam Lee, John Lui (CUHK) David Yau (Purdue)

Information, Incentives, and Mechanism Design

Presentation transcript:

Potential games are necessary to ensure pure Nash equilibria in cost sharing games

Model for distributed resource allocation problems. Self-interested agents make decisions and share the resulting cost. cost sharing games Network formation [ Anshelevich et al ] S1 S2 D1 D ?+?

cost sharing games Network formation [ Anshelevich et al ] S1 S2 D1 D A Nash equilibrium Also optimal! 1+5 Unique Nash equilibrium Suboptimal

cost sharing games Key feature: Distribution rules outcome! Network formation [ Anshelevich et al ] ?+? S1 S2 D1 D

cost sharing games Network formation games Facility location games Congestion games Routing games Multicast games Coverage games … [ Anshelevich et al ] [ Corbo and Parkes 2005 ] [ Fiat et al ] [ Albers 2009 ] [ Chen and Roughgarden 2009 ] [ Epstein, Feldman, and Mansour 2009 ] [ … ] [ Rosenthal 1973 ] [ Milchtaich 1996 ] [ Christodoulou and Koutsoupias 2005 ] [ Suri, Tóth, and Zhou 2007 ] [Bhawalkar, Gairing, and Roughgarden 2010 ] [ … ] [ Roughgarden and Tardos 2002 ] [ Kontogiannis and Spirakis 2005 ] [ Awerbuch, Azar, and Epstein 2005 ] [ Chen, Chen, and Hu 2010 ] [ … ] [ Marden and Wierman 2008 ] [ Panagopoulou and Spirakis 2008 ] [ … ] [ Vetta 2002 ] [ Hoefer 2006 ] [ Dürr and Thang 2006 ] [ Chekuri et al ] [ Hansen and Telelis 2008 ] [ … ] [ Chekuri et al ] [ Cardinal and Hoefer 2010 ] [ Bilò et al ] [ Buchbinder et al ] [ … ] [ Johari and Tsitsiklis 2004 ] [ Panagopoulou and Spirakis 2008 ] [ Marden and Effros 2009 ] [ Harks and Miller 2011 ] [ von Falkenhausen and Harks 2013 ] [ … ] Key feature: Distribution rules outcome!

Most prior work studies two distribution rules Marginal Contribution (MC) [ Wolpert and Tumer 1999 ] average marginal contribution over player orderings Shapley Value (SV) [ Shapley 1953 ] externality experienced by all other players

Most prior work studies two distribution rules Marginal Contributions (MC+) [ Wolpert and Tumer 1999 ] average marginal contribution over player orderings Shapley Values (SV+) [ Shapley 1953 ] externality experienced by all other players Both guarantee PNE in all games! Question: Are there other such distribution rules? Short answer: NO! for any fixed cost functions

don‘t guarantee PNE in all games guarantee PNE in all games SV+ don‘t guarantee PNE in all games guarantee PNE in all games MC+ all distribution rules SV+ MC+ guarantee potential game 1 2 don‘t guarantee PNE in all games guarantee PNE in all games ?

set of players set of resources S1S1 S2S2 D1 D2 Example: Formal model “welfare” = revenue / negative cost

Recall:

“all games”

don‘t guarantee PNE in all games guarantee PNE in all games The inspiration for our work [ Chen, Roughgarden, and Valiant 2010 ] budget- balanced guarantee potential game don‘t guarantee PNE in all games guarantee PNE in all games Our characterization ? actual welfare distributed ?

don‘t guarantee PNE in all games guarantee PNE in all games don‘t guarantee PNE in all games guarantee PNE in all games The inspiration for our work [ Chen, Roughgarden, and Valiant 2010 ] budget- balanced guarantee potential game don‘t guarantee PNE in all games guarantee PNE in all games Our characterizations

Tractability Consequences Efficiency Incentive compatibility Budget- balance Four other important properties: don‘t guarantee PNE in all games guarantee PNE in all games

Tractability Consequences Efficiency Incentive compatibility Budget- balance Four other important properties: Easier to control budget-balance More tractable “preprocessing” don‘t guarantee PNE in all games guarantee PNE in all games don‘t guarantee PNE in all games guarantee PNE in all games exponential time!

Tractability Consequences Efficiency Incentive compatibility Budget- balance Four other important properties: private values Future work: Design incentive compatible cost sharing mechanisms for a noncooperative setting

“coalition” “contribution of the coalition” Proof sketch [ Shapley 1953 ]

Proof sketch no yes DECOMPOSITON 1

Proof sketch DECOMPOSITON Proof: Establish a “fairness” condition 1 CONSISTENCY 2

Potential games are necessary to ensure pure Nash equilibria in cost sharing games