network economics -- lecture 2: incentives in online...

NetworkEconomics--

Lecture2:IncentivesinonlinesystemsI:freeridingandeffort

elicitation

PatrickLoiseauEURECOMFall2016

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References• Main:

– N.Nisam,T.Roughgarden,E.Tardos andV.Vazirani (Eds).“AlgorithmicGameTheory”,CUP2007.Chapters23(seealso27).• Availableonline:

http://www.cambridge.org/journals/nisan/downloads/Nisan_Non-printable.pdf

• Additional:– Yiling ChenandArpita Gosh,“SocialComputingandUserGenerated

Content,”EC’13tutorial• Slidesathttp://www.arpitaghosh.com/papers/ec13_tutorialSCUGC.pdf and

http://yiling.seas.harvard.edu/wp-content/uploads/SCUGC_tutorial_2013_Chen.pdf

– M.Chiang.“NetworkedLife,20QuestionsandAnswers”,CUP2012.Chapters3-5.• Seethevideosonwww.coursera.org

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Outline

1. Introduction2. TheP2Pfilesharinggame3. Free-ridingandincentivesforcontribution4. Hiddenactions:theprincipal-agentmodel

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Outline

1. Introduction2. TheP2Pfilesharinggame3. Free-ridingandincentivesforcontribution4. Hiddenactions:theprincipal-agentmodel

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Onlinesystems• Resources

– P2Psystems• Information

– Ratings– Opinionpolls

• Content(user-generatedcontent)– P2Psystems– Reviews– Forums– Wikipedia

• Labor(crowdsourcing)– AMT

• Inallthesesystems,thereisaneedforuserscontribution

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P2Pnetworks• Firstones:Napster(1999),Gnutella(2000)– Free-ridingproblem

• Manyusersacrosstheglobeself-organizingtosharefiles– Anonymity– One-shotinteractionsàDifficulttosustaincollaboration

• Exacerbatedby– Hiddenactions(nondetectable defection)– Cheappseudonyms(multipleidentitieseasy)

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Incentivemechanisms

• Goodtechnologyisnotenough• P2Pnetworksneedincentivemechanismstoincentivizeuserstocontribute– Reputation(KaZaA)– Currency(calledscrip)– Barter(BitTorrent)– directreciprocity

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Extensions

• Otherfree-ridingsituations– E.g.,mobilead-hocnetworks,P2Pstorage

• Richstrategyspace– Share/notshare– Amountofresourcescommitted– Identitymanagement

• Otherapplicationsofincentives/reputationsystems– Onlineshopping,forums,etc.

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Outline

1. Introduction2. TheP2Pfilesharinggame3. Free-ridingandincentivesforcontribution4. Hiddenactions:theprincipal-agentmodel

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TheP2Pfile-sharinggame

• Peer– Sometimesdownloadà benefit– Sometimesuploadà cost

• Oneinteraction~prisoner’sdilemmaC D

C

D

2,2 -1,3

0,03,-110

Prisoner’sdilemma

• Dominantstrategy:D• Sociallyoptimal(C,C)

• Singleshotleadsto(D,D)– Sociallyundesirable

• Iteratedprisoner’sdilemma– Tit-for-tatyieldssociallyoptimaloutcome

C D

C

D

2,2 -1,3

0,03,-1

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P2P

• Manyusers,randominteractions

• Directreciprocitydoesnotscale

Feldmanetal.2004

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P2P

• Directreciprocity– EnforcedbyBittorrent atthescaleofonefilebutnotoverseveralfiles

• Indirectreciprocity– Reputationsystem– Currencysystem

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Howtotreatnewcomers

• P2Phashighturnover• Ofteninteractwithstrangerwithnohistory

• TFTstrategywithCwithnewcomers– Encouragenewcomers– BUTFacilitateswhitewashing

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Outline

1. Introduction2. TheP2Pfilesharinggame3. Free-ridingandincentivesforcontribution4. Hiddenactions:theprincipal-agentmodel

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Reputation

• Longhistoryoffacilitatingcooperation(e.g.eBay)

• Ingeneralcoupledwithservicedifferentiation– Goodreputation=goodservice– Badreputation=badservice

• Ex:KaZaA

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Trust

• EigenTrust (SepKamvar,MarioSchlosser,andHectorGarcia-Molina,2003)– Computesaglobaltrustvalueofeachpeerbasedonthelocaltrustvalues

• Usedtolimitmalicious/inauthenticfiles– Defenseagainstpollutionattacks

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Attacksagainstpollutionsystems

• Whitewashing• Sybilattacks• Collusion• Dishonestfeedback

• Seenextlecture…• Thislecture:howreputationhelpsinelicitingeffort

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AminimalistP2Pmodel

• Largenumberofpeers(players)• Peeri hastypeθi (~“generosity”)• Actionspace:contributeorfree-ride• x:fractionofcontributingpeersà1/x:costofcontributing

• Rationalpeer:– Contributeifθi >1/x– Free-rideotherwise 19

Contributionswithnoincentivemechanism

• Assumeuniformdistributionoftypes

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Contributionswithnoincentivemechanism(2)

• Equilibria stability

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Contributionswithnoincentivemechanism(3)

• Equilibria computation

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Contributionswithnoincentivemechanism(4)

• Result:Thehigheststableequilibriumcontributionlevelx1 increaseswithθm andconvergestooneasgoesθm toinfinitybutfallstozeroifθm <4

• Remark:ifthedistributionisnotuniform:thegraphicalmethodstillapplies

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Overallsystemperformance

• W=ax-(1/x)x=ax-1

• Evenifparticipationprovideshighbenefits,thesystemmaycollapse

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ReputationandservicedifferentiationinP2P

• Considerareputationsystemthatcancatchfree-riderswithprobabilitypandexcludethem– Alternatively:catchallfree-ridersandgivethemservicealteredby(1-p)

• Twoeffects– Loadreduced,hencecostreduced– Penaltyintroducesathreat

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Equilibriumwithreputation

• Q:individualbenefit• R:reducedcontribution• T:threat

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Equilibriumwithreputation(2)

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Systemperformancewithreputation

• W=x(Q-R)+(1-x)(Q-T)=(ax-1)(x+(1-x)(1-p))

• Trade-off:Penaltyonfreeridersincreasesxbutentailssocialcost

• Ifp>1/a,thethreatislargerthanthecostà Nofreerider,optimalsystemperformancea-1

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FOX(FairOptimaleXchange)

• Theoreticalapproach• Assumesallpeerarehomogeneous,withcapacitytoservekrequestsinparallelandseektominimizecompletiontime

• FOX:distributedsynchronizedprotocolgivingtheoptimum– i.e.,allpeerscanachieveoptimumiftheycomply

• “grimtrigger”strategy:eachpeercancollapsethesystemifhefindsadeviatingneighbor

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FOXequilibrium

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Outline

1. Introduction2. TheP2Pfilesharinggame3. Free-ridingandincentivesforcontribution4. Hiddenactions:theprincipal-agentmodel

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Hiddenactions• InP2P,manystrategicactionsarenotdirectlyobservable– Arrival/departure– Messageforwarding

• Samewithmanyothercontexts– Packetforwardinginad-hocnetworks– Worker’seffort

• Moralhazard:situationinwhichapartyismorewillingtotakeariskknowingthatthecostwillbesupported(atleastinpart)byothers– E.g.,insurance 32

Principal-agentmodel• Aprincipalemploysasetofnagents:N={1,…,n}• ActionsetAi={0,1}• Costc(0)=0,c(1)=c>0• Theactionsofagentsdetermine(probabilistically)an

outcomeoin{0,1}• Principalvaluationofsuccess:v>0(nogainincaseof

failure)• Technology(orsuccessfunction)t(a1,…,an):probabilityof

success

• Remark:manydifferentmodelsexist– Oneagent,differentactionsets– Etc.

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Read-oncenetworks

• Onegraphwith2specialnodes:sourceandsink• Eachagentcontrols1link• Agentsaction:– loweffortà succeedwithprobabilityγ in(0,1/2)– Higheffortà succeedwithprobability1-γin(1/2,1)

• Theprojectsucceedsifthereisasuccessfulsource-sinkpath

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Example

• ANDtechnology

• ORtechnology

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Contract

• Theprincipalagentcandesigna“contract”– Paymentofpi≥0uponsuccess– Nothinguponfailure

• Theagentsareinagame:

• Theprincipalwantstodesignacontractsuchthathisexpectedprofitismaximized

ui (a) = pit(a)− c(ai )

u(a,v) = t(a) ⋅ v− pii∈N∑

%

&'

(

)*

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Definitionsandassumptions

• Assumptions:– t(1,a-i)>t(0,a-i)foralla-i– t(a)>0foralla

• Definition:themarginalcontributionofagenti givena-i is

• Increaseinsuccessprobabilityduetoi’seffort

Δi (a−i ) = t(1,a−i )− t(0,a−i )

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Individualbestresponse

• Givena-i,agent’si beststrategyis

ai =1 if pi ≥c

Δi (a−i )

ai = 0 if pi ≤c

Δi (a−i )

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Bestcontractinducinga

• Thebestcontractfortheprincipalthatinducesa asanequilibriumconsistsin– fortheagentschoosingai=0– fortheagentschoosingai=1pi =

cΔi (a−i )

pi = 0

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Bestcontractinducinga (2)

• Withthisbestcontract,expectedutilitiesare– fortheagentschoosingai=0

– fortheagentschoosingai=1

– fortheprincipal

ui = c ⋅t(1,a−i )Δi (a−i )

−1$

%&

'

()

ui = 0

u(a,v) = t(a) ⋅ v− cΔi (a−i )i:ai=1

∑%

&''

(

)**

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Principal’sobjective

• Choosingtheactionsprofilea* thatmaximizeshisutilityu(a,v)

• EquivalenttochoosingthesetS* ofagentswithai=1

• Dependsonvà S*(v)

• Wesaythattheprincipalcontractswithi ifai=1

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Hiddenvs observableactions

• Hiddenactions:

ifai=1and0otherwise

• Ifactionswereobservable– Givepi=ctohigh-effortagentsregardlessofsuccess– Yieldsfortheprincipalautilityequaltosocialwelfare

à Choosea tomaximizesocialwelfare

u(a,v) = t(a) ⋅ v− cΔi (a−i )i:ai=1

∑%

&''

(

)**

ui = c ⋅t(1,a−i )Δi (a−i )

−1$

%&

'

()

u(a,v) = t(a) ⋅ v− ci:ai=1∑

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(POU)PriceofUnaccountability

• S*(v):optimalcontractinhiddencase• S0*(v):optimalcontractinobservablecase

• Definition:thePOU(t)ofatechnologytisdefinedastheworst-caseratioovervoftheprincipal’sutilityintheobservableandhiddenactionscases

POU(t) = supv>0

t(S0*(v)) ⋅ v− c

i∈S0* (v)∑

t(S*(v)) ⋅ v− ct(S*(v))− t(S*(v) \ {i})i∈S* (v)∑

%

&'

(

)*43

Remark

• POU(t)>1

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Optimalcontract

• Wewanttoanswerthequestions:

• Howtoselecttheoptimalcontract(i.e.,theoptimalsetofcontractingagents)?

• Howdoesitchangewiththeprincipal’svaluationv?

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Monotonicity

• Theoptimalcontractsweaklyimproveswhenvincreases:– Foranytechnology,inboththehidden- andobservable-actionscases,theexpectedutilityoftheprincipal,thesuccessprobabilityandtheexpectedpaymentoftheoptimalcontractareallnon-decreasingwhenvincreases

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Proof

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Proof(2)

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Consequences

• Anonymoustechnology:thesuccessprobabilityissymmetricintheplayers

• Fortechnologiesforwhichthesuccessprobabilitydependsonlyonthenumberofcontractedagents(e.g.AND,OR),thenumberofcontractedagentsisnon-decreasingwhenvincreases

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OptimalcontractfortheANDtechnology

• Theorem:ForanyanonymousANDtechnologywithγ =γi =1-δi foralli– Thereexistsavaluationfinitev*suchthatforanyv<v*,itisoptimaltocontractwithnoagentandforanyv>v*,itisoptimaltocontractwithallagents(forv=v*,bothcontractsareoptimal)

– Thepriceofunaccountabilityis

POU =1γ−1

"

#$

%

&'

n−1

+ 1− γ1−γ

"

#$

%

&'

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Remarks

• ProofinM.Babaioff,M.FeldmanandN.Nisan,“CombinatorialAgency”,inProceedingsofEC2006.

• POUisnotbounded!–Monitoringcanbebeneficial,evenifcostly

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Example

• n=2,c=1,γ=1/4• Computeforallnumberofagents– t– Δ– Utilityofprincipal

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OptimalcontractfortheORtechnology

• Theorem:ForanyanonymousORtechnologywithγ =γi =1-δi foralli– Thereexistfinitepositivevaluesv1,…,vn suchthatforanyvin(vk,vk+1),itisoptimaltocontractkagent.(Forv<v0,itisoptimaltocontract0agent,forv>vn,itisoptimaltocontractnagentandforv=vk,theprincipalisindifferentbetweencontractingk-1orkagents.)

– Thepriceofunaccountabilityisupperboundedby5/2

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Example

• n=2,c=1,γ=1/4• Computeforallnumberofagents– t– Δ– Utilityofprincipal

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Illustration

• Numberofcontractedagents

v

3

0

gamma

200

150

0.4

100

50

0.30

0.20.10

2 1 0

3

12000

6000

8000

4000

2000

gamma

00.4 0.45

10000

0.3 0.350.250.2

Figure 3: Number of agents in the optimal contractof the AND (left) and OR (right) technologies with 3players, as a function of γ and v. AND technology: either0 or 3 agents are contracted, and the transition value ismonotonic in γ. OR technology: for any γ we can see alltransitions.

3.1 AND and OR TechnologiesLet us start with a direct and full analysis of the AND

and OR technologies for two players for the case γ = 1/4and c = 1.

Example 1. AND technology with two agents, c =1, γ = 1/4: we have t0 = γ2 = 1/16, t1 = γ(1 − γ) = 3/16,and t2 = (1 − γ)2 = 9/16 thus ∆0 = 1/8 and ∆1 = 3/8.The principal has 3 possibilities: contracting with 0, 1, or 2agents. Let us write down the expressions for his utility inthese 3 cases:

• 0 Agents: No agent is paid thus and the principal’sutility is u0 = t0 · v = v/16.

• 1 Agent: This agent is paid p1 = c/∆0 = 8 on successand the principal’s utility is u1 = t1(v−p1) = 3v/16−3/2.

• 2 Agents: each agent is paid p2 = c/∆1 = 8/3 onsuccess, and the principal’s utility is u2 = t2(v−2p2) =9v/16 − 3.

Notice that the option of contracting with one agent is alwaysinferior to either contracting with both or with none, and willnever be taken by the principal. The principal will contractwith no agent when v < 6, with both agents whenever v > 6,and with either non or both for v = 6.

This should be contrasted with the non-strategic case inwhich the principal completely controls the agents (and bearstheir costs) and thus simply optimizes globally. In this casethe principal will make both agents exert effort whenever v ≥4. Thus for example, for v = 6 the globally optimal decision(non-strategic case) would give a global utility of 6 · 9/16 −2 = 11/8 while the principal’s decision (in the agency case)would give a global utility of 3/8, giving a ratio of 11/3.

It turns out that this is the worst price of unaccountabilityin this example, and it is obtained exactly at the transitionpoint of the agency case, as we show below.

Example 2. OR technology with two agents, c = 1,γ = 1/4: we have t0 = 1 − (1 − γ)2 = 7/16, t1 = 1 −γ(1 − γ) = 13/16, and t2 = 1 − γ2 = 15/16 thus ∆0 = 3/8and ∆1 = 1/8. Let us write down the expressions for theprincipal’s utility in these three cases:

• 0 Agents: No agent is paid and the principal’s utilityis u0 = t0 · v = 7v/16.

• 1 Agent: This agent is paid p1 = c/∆0 = 8/3 onsuccess and the principal’s utility is u1 = t1(v − p1) =13v/16 − 13/6.

• 2 Agents: each agent is paid p2 = c/∆1 = 8 on suc-cess, and the principal’s utility is u2 = t2(v − 2p2) =15v/16 − 15/2.

Now contracting with one agent is better than contractingwith none whenever v > 52/9 (and is equivalent for v =52/9), and contracting with both agents is better than con-tracting with one agent whenever v > 128/3 (and is equiv-alent for v = 128/3), thus the principal will contract withno agent for 0 ≤ v ≤ 52/9, with one agent for 52/9 ≤ v ≤128/3, and with both agents for v ≥ 128/3.

In the non-strategic case, in comparison, the principal willmake a single agent exert effort for v > 8/3, and the secondone exert effort as well when v > 8.

It turns out that the price of unaccountability here is19/13, and is achieved at v = 52/9, which is exactly thetransition point from 0 to 1 contracted agents in the agencycase. This is not a coincidence that in both the AND andOR technologies the POU is obtained for v that is a transi-tion point (see full proof in [2]).

Lemma 1. For any given technology (t, c⃗) the price of un-accountability POU(t, c⃗) is obtained at some value v whichis a transition point, of either the agency or the non-strategiccases.

Proof sketch: We look at all transition points in both cases.For any value lower than the first transition point, 0 agentsare contracted in both cases, and the social welfare ratiois 1. Similarly, for any value higher than the last transi-tion point, n agents are contracted in both cases, and thesocial welfare ratio is 1. Thus, we can focus on the inter-val between the first and last transition points. Between anypair of consecutive points, the social welfare ratio is betweentwo linear functions of v (the optimal contracts are fixed onsuch a segment). We then show that for each segment, thesuprimum ratio is obtained at an end point of the segment(a transition point). As there are finitely many such points,the global suprimum is obtained at the transition point withthe maximal social welfare ratio. ✷

We already see a qualitative difference between the ANDand OR technologies (even with 2 agents): in the first caseeither all agents are contracted or none, while in the secondcase, for some intermediate range of values v, exactly oneagent is contracted. Figure 3 shows the same phenomenafor AND and OR technologies with 3 players.

Theorem 1. For any anonymous AND technology7:

• there exists a value8 v∗ < ∞ such that for any v < v∗it is optimal to contract with no agent, for v > v∗ it isoptimal to contract with all n agents, and for v = v∗,both contracts (0, n) are optimal.

7AND technology with any number of agents n and any γ,and any identical cost c.8v∗ is a function of n, γ, c.

23

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