On Threshold Behavior in Query Incentive Networks Arcaute On Threshold Behavior in Query Incentive Kirsch Kumar Liben-Nowell Networks Vassilvitskii Motivation Trusted answers? Ask your friends! Esteban Arcaute 1 Adam Kirsch 2 Ravi Kumar 3 Online friends? Use incentives! David Liben-Nowell 4 Sergei Vassilvitskii 1 Model Mathematical Formulation Branching Process 1 Stanford University 2 Harvard University and Framework Objective 3 Yahoo! Research 4 Carleton College Results Previous Results Our Results Discussion The 8th ACM Conference on Electronic Commerce Current Research EC’07
On Threshold Behavior in Outline Query Incentive Networks Arcaute Kirsch 1 Motivation Kumar Trusted answers? Ask your friends! Liben-Nowell Vassilvitskii Online friends? Use incentives! Motivation Trusted answers? Ask your friends! 2 Model Online friends? Use incentives! Mathematical Formulation Model Branching Process and Framework Mathematical Formulation Objective Branching Process and Framework Objective Results Results 3 Previous Results Our Results Previous Results Discussion Our Results Current Research Discussion Current Research
On Threshold Behavior in Some Have Questions Query Incentive Networks Others Answers Arcaute Kirsch Kumar Liben-Nowell Vassilvitskii Motivation Model introduced by Kleinberg and Raghavan [FOCS ’05] Trusted answers? Ask your friends! Online friends? Use incentives! Model • Assume that a user, say u , of a social network has a Mathematical Formulation question (e.g. Where to find a good physician?) Branching Process and Framework Objective • Suppose that some subset of users have an answer Results Previous Results Our Results • How would u retrieve an answer from those individuals? Discussion Current Research
On Threshold Behavior in An Answer or The Answer Query Incentive Networks Differences Arcaute Kirsch Kumar Liben-Nowell Vassilvitskii To get an answer, u could: Motivation • use a search engine; or Trusted answers? Ask your friends! Online friends? Use • ask friends. incentives! Model What’s the difference? Mathematical Formulation Branching Process and Framework • Search engine: many answers but may not be reliable Objective • Friends: trusted answers but may not have any Results Previous Results Our Results Discussion Current Research Not enough friends? Reach friends’ friends! ⇒ “web of trust”.
On Threshold Behavior in Ask Your Friends, Please Query Incentive Networks Arcaute Kirsch Kumar Liben-Nowell Vassilvitskii • Reaching friends’ friends through incentives Motivation Trusted answers? Ask your friends! • Offer payment for answers Online friends? Use incentives! → utility transfer ֒ Model Mathematical Formulation • Users act as strategic agents Branching Process and Framework Objective Results Natural question: how much should u offer? Previous Results Our Results Discussion Current Research
On Threshold Behavior in Informal Description Query Incentive Networks Key Ideas to Model Arcaute Kirsch Kumar Liben-Nowell Vassilvitskii Motivation Key features from Kleinberg and Raghavan’s model. Trusted answers? Ask your friends! • Nodes and answers: Online friends? Use incentives! • all answers are created equal Model • each person, independently, has an answer Mathematical Formulation with probability 1 Branching Process n and Framework Objective • Users aware of only local topology Results ֒ → model with a random graph Previous Results Our Results • Providing incentives to answer, not creating a market Discussion Current Research
On Threshold Behavior in Network, Agents and Incentives Query Incentive Networks Arcaute Kirsch • Underlying network: complete d -ary tree ( d > 1) Kumar Liben-Nowell • Root: special node with query (question) Vassilvitskii • Realized network: each node has (independently) Motivation Trusted answers? 0 ≤ i ≤ d children with distribution C Ask your friends! Online friends? Use identities of nodes chosen uniformly at random incentives! Model Mathematical Formulation Branching Process and Framework Objective Results Previous Results Our Results Discussion Current Research
On Threshold Behavior in Network, Agents and Incentives Query Incentive Networks Arcaute Kirsch • Underlying network: complete d -ary tree ( d > 1) Kumar Liben-Nowell • Root: special node with query (question) Vassilvitskii • Realized network: each node has (independently) Motivation Trusted answers? 0 ≤ i ≤ d children with distribution C Ask your friends! Online friends? Use identities of nodes chosen uniformly at random incentives! Model Mathematical Formulation Branching Process and Framework Objective Results Previous Results Our Results Discussion Current Research
On Threshold Behavior in Network, Agents and Incentives Query Incentive Networks Arcaute Kirsch • Underlying network: complete d -ary tree ( d > 1) Kumar Liben-Nowell • Root: special node with query (question) Vassilvitskii • Realized network: each node has (independently) Motivation Trusted answers? 0 ≤ i ≤ d children with distribution C Ask your friends! Online friends? Use identities of nodes chosen uniformly at random incentives! Model Mathematical Formulation Branching Process and Framework Objective Results Previous Results Our Results Discussion Current Research
On Threshold Behavior in Completing the Model Query Incentive Networks For the incentives: Arcaute Kirsch Kumar • parent node offers reward for answer to children Liben-Nowell Vassilvitskii • if agent has an answer, communicates it to parent Motivation • if there are many answers, choose one uniformly at Trusted answers? Ask your friends! random Online friends? Use incentives! • if providing answer, pay unit cost Model Mathematical Formulation Branching Process and Framework Objective Results Previous Results Our Results Discussion Current Research
On Threshold Behavior in Completing the Model Query Incentive Networks For the incentives: Arcaute Kirsch Kumar • parent node offers reward for answer to children Liben-Nowell Vassilvitskii • if agent has an answer, communicates it to parent Motivation • if there are many answers, choose one uniformly at Trusted answers? Ask your friends! random Online friends? Use incentives! • if providing answer, pay unit cost Model Mathematical Formulation Branching Process and Framework Formally, if a node is offered r and doesn’t have an answer Objective Tradeoff faced by the node: if it offers f ( r ) , Results Previous Results Our Results • amount it keeps r − f ( r ) − 1 Discussion Current Research • probability of finding an answer in subtree increases with f ( r ) Solution concept: Nash Equilibrium
On Threshold Behavior in Schema of Incentives Query Incentive Networks Arcaute Kirsch Kumar offer r Liben-Nowell Vassilvitskii offer f ( r ) Motivation Trusted answers? Ask your friends! offer f ( f ( r )) Online friends? Use incentives! Model Mathematical Formulation Branching Process and Framework Objective Results Previous Results Our Results Discussion Current Research
On Threshold Behavior in Schema of Incentives Query Incentive Networks Arcaute Kirsch Kumar offer r Liben-Nowell Vassilvitskii offer f ( r ) Motivation Trusted answers? Ask your friends! offer f ( f ( r )) Online friends? Use incentives! Model Mathematical Formulation Branching Process payoffs: and Framework Objective Results r − f ( r ) − 1 Previous Results Our Results Discussion f ( r ) − f ( f ( r )) − 1 Current Research f ( f ( r )) − 1
On Threshold Behavior in Model as Branching Process Query Incentive Networks Parameters Arcaute Kirsch • C distribution with support { 0 , ..., d } Kumar Liben-Nowell let b be its expectation Vassilvitskii • Realized network: realization of branching process Motivation Trusted answers? according to C Ask your friends! Online friends? Use • identities of nodes chosen uniformly at random incentives! Model Mathematical Formulation Branching Process and Framework b > 1 ⇒ infinite network with constant probability Objective Results Previous Results Our Results • Average number of nodes in the first k layers: Discussion Current Research 1 − b k + 1 � b k � = Θ 1 − b • In Θ( log n ) layers, one answer with constant probability
On Threshold Behavior in Objective Query Incentive Networks Arcaute Kirsch Kumar Liben-Nowell • Given Vassilvitskii • probability of success 1 > σ > 0; Motivation • the distribution C ; Trusted answers? Ask your friends! • the rarity of the answer n ; and Online friends? Use incentives! • agents play a Nash Equilibrium given by the function f Model Mathematical Formulation Branching Process and Framework • Find minimum offer R σ, C ( n ) to get answer with Objective probability at least σ Results Previous Results Our Results Discussion • Study dependency of R σ, C ( n ) on C and σ Current Research
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