IntroductionThesis Work
Online Mechanisms with out Money
Online Mechanisms without Money for Assignmentof Objects to Strategic Agents
Sujit Prakash GujarResearch Supervisor: Y Narahari
sujit,[email protected] Lab
Department of Computer Science and AutomationIndian Institute of Science, Bangalore-12
FIRST ELECTRICAL SCIENCE DIVISIONAL SYMPOSIUM
22 January, 2010
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 1 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Agenda
Motivation and Introduction
Outline of The Thesis
Online Mechanisms Without Money.
Online Assignment MechanismsOnline House Allocation MechanismsOnline Matchings
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 2 / 19
IntroductionThesis Work
Online Mechanisms with out Money
MotivationOnline SettingsIntroduction to Mechanism Design Theory
Motivation
Campus recruitment
Dorm assignment
Intern-Hospital assignment
Wiki: some tasks need volunteers
In general, assignment of heterogeneous objects to competing agents
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 3 / 19
IntroductionThesis Work
Online Mechanisms with out Money
MotivationOnline SettingsIntroduction to Mechanism Design Theory
Online Settings
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 4 / 19
IntroductionThesis Work
Online Mechanisms with out Money
MotivationOnline SettingsIntroduction to Mechanism Design Theory
Online Settings
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 4 / 19
IntroductionThesis Work
Online Mechanisms with out Money
MotivationOnline SettingsIntroduction to Mechanism Design Theory
Online Settings
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 4 / 19
IntroductionThesis Work
Online Mechanisms with out Money
MotivationOnline SettingsIntroduction to Mechanism Design Theory
Online Settings
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 4 / 19
IntroductionThesis Work
Online Mechanisms with out Money
MotivationOnline SettingsIntroduction to Mechanism Design Theory
Intellectual Challenge
Strategic players
Private preferences
No money
Online nature of the problem
Mechanism Design is a natural tool to apply
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 5 / 19
IntroductionThesis Work
Online Mechanisms with out Money
MotivationOnline SettingsIntroduction to Mechanism Design Theory
Mechanism Design
Game Theory: Analysis of strategic interaction among players
Mechanism Design: Reverse engineering of games
Mechanism Design is the art of designing rules of a game to achievea specific outcome in presence of multiple self-interested agents,each with private information about their preferences.
Nobel Prize in Economics Sciences, 2007: Hurwicz, Myerson, Maskin
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 6 / 19
IntroductionThesis Work
Online Mechanisms with out Money
My Thesis
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 7 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
Markets without Money
One Sided Markets
Objects assignment without initial endowmentsOnline Assignment Mechanisms
Objects assignment with initial endowmentsOnline House Allocation Mechanisms
Two Sided Markets
Online Matchings
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 8 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
Online Assignment Mechanisms
N = {A1, A2, . . . ,An}, Set of agents
M = {1, 2, . . . ,m} Set of distinct objects
Agents have strict preferences
When the agents and the objects are static:
Svenssons1: Any strategyproof mechanism that satisfies neutralityand no-bossy properties must be necessarily a Serial Dictatorship.
Online setting: Agent i arrives at time ai and departs system at di
1L.-G. Svensson. strategyproof allocation of indivisible goods. Social Choice andWelfare, 16(4):557-567, 1999.
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 9 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
Our Results
When arrival-departure schedules are endogenous
Lemma 1
Any strategyproof mechanism that satisfies neutrality and non-bossynessmust be necessarily Online Serial Dictatorship.
When arrival-departure schedules are exogenous
Theorem 1
Any strategyproof mechanism that satisfies neutrality and non-bossynessmust be necessarily Arrival Priority Serial Dictatorship
We also call Arrival Priority Serial Dictatorship as Greedymechanism
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 10 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
Performance of Greedy
Rank of an assignment: average rank that an agent assigns to theobject he receives in the assignment
Consider an example with n = m = 4
Example
A1 : 1 � 4 � 2 � 3, a1 = d1 = 1
A2 : 1 � 2 � 3 � 4, a2 = d2 = 2
A3 : 2 � 1 � 3 � 4, a3 = d3 = 3
A4 : 3 � 2 � 1 � 4, a4 = d4 = 4
Rank of Greedy can be as bad as n2
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 11 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
Scoring Rule Based Mechanism
Heuristic mechanism
Preserves most wanted items, if some agent is fine with an objectthat is in general not desirable by the rest of the agents
S(j) =∑
r Pj(r)r
For an agent, upon arrival allocate an item i such that
i ∈ arg min{rank(j)− S(j)}
Not strategyproof
However, performs much better on rank analysis as compared toGreedy
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 12 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
Simulation Results
Figure: Rank efficiency vs n.
SR perform better on rank analysis atleast by 10% over Greedy
Figure: Rank efficiency with strategic agents
If small fraction of agents are strategic, SRis better for everybody
SR is better even in the presence ofstrategic agents
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 13 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
House Allocation Mechanisms
Shapley Scarf Economy2
Static case: TTCA
Online case: Repeated TTCA not strategyproof
× No online Pareto efficient mechanism√
Partition agents. Agents in a partition execute TTCA
2Lloyd Shapley and Herbert Scarf. On cores and indivisibility. Journal ofMathematical Economics, 1(1):23-37, March 1974.
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 14 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
Stable Matchings
Gale-Shapley3 abstracted this problem as marriage problem
M Set of Men. Static and strategic
W Set of Women. Dynamic but truthful
Even in the presence of non-strategic agents, no online mechanism isstable
We allow static agents to use substitutes
3D. Gale and L. S. Shapley: ”College Admissions and the Stability of Marriage”,American Mathematical Monthly 69, 9-14, 1962.
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 15 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
Results So far
We proposed GSODAS (General period Online Deferred Acceptancewith Substitutes)
We showed,
GSODAS is strategyproofmatching is stable for the men who are matched by our algorithmNo other algorithm can yield stability better than GSODAS
We are also working on algorithms achieving better rank efficiencyusing CONSENSUS type algorithms from online stochasticcombinatorial optimization
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 16 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
Publications based on Thesis Work
Dinesh Garg, Y Narahari, Sujit Gujar, “Foundations of MechanismDesign: A tutorial, Part 1, 2”. Sadhana - Indian AcademyProceedings in Engineering Sciences, April 2008.Sujit Gujar and Y. Narahari, “Optimal Multi-Unit CombinatorialAuctions with Single Minded Bidders”. The 11th IEEE Conferenceon Commerce and Enterprise Computing (CEC’09), 2009, pp.74-81.Sujit Gujar and Y. Narahari, “Redistribution Mechanisms forAssignment of Heterogeneous Objects”. Formal Approaches toMulti-Agent Systems, (FAMAS’09). Torino, Itly.Sujit Gujar and Y Narahari, “Redistribution of VCG Payments inAssignment of Heterogeneous Objects”. In Proceedings of the 4thInternational Workshop on Internet and Network Economics(WINE), 2008, pp 438-445.James Zou, Sujit Gujar, David Parkes, “ Tolerable Manipulations:New Approach to Dynamic Allocation Without Money”, TechnicalReportSujit Gujar, David Parkes, “Dynamic Matchings”, Working Paper
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 17 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
Questions?
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 18 / 19
IntroductionThesis Work
Online Mechanisms with out Money
Markets without MoneyAssignment MechanismsOnline House Allocation MechanismsOnline Matchings
Thank You!!!
Sujit Gujar (CSA, IISc) Online Mechanisms without Money 22 January, 2010 19 / 19
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