online mechanisms without money for assignment of objects to...

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



Agenda

Motivation and Introduction

Outline of The Thesis

Online Mechanisms Without Money.

Online Assignment MechanismsOnline House Allocation MechanismsOnline Matchings




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





Online Settings





Intellectual Challenge

Strategic players

Private preferences

No money

Online nature of the problem

Mechanism Design is a natural tool to apply





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




My Thesis




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





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.





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





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





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





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





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.





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.





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





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





Questions?





Thank You!!!


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