1. Gossip-Based Aggregation of Trust in Decentralized Reputation Systems Ariel D. Procaccia, Yoram Bachrach, and Jeffrey S. Rosenschein

2. Lecture Outline Introduction Gossip-based algorithms Our approach Features Motivates truthfulness Impervious to attacks Conclusions Introduction Gossip-based algorithms Our approach Features Motivates truthfulness Impervious to attacks Conclusions IntroductionGossip-BasedOur ApproachFeaturesConclusions

3. Background Multiagent environments are often teeming with self-interested agents which are continually interacting. Agents may be tempted to employ deceit, but dishonest agents can expect their victims to retaliate. This motivates cooperation and trustworthiness. Multiagent environments are often teeming with self-interested agents which are continually interacting. Agents may be tempted to employ deceit, but dishonest agents can expect their victims to retaliate. This motivates cooperation and trustworthiness. IntroductionGossip-BasedOur ApproachFeaturesConclusions

4. Reputation Systems As number of agents grows, agents have smaller chance to interact with agents they know. Building trust becomes harder. Reputation systems collect and spread reports among agents. Agents learn from others’ experience. As number of agents grows, agents have smaller chance to interact with agents they know. Building trust becomes harder. Reputation systems collect and spread reports among agents. Agents learn from others’ experience. IntroductionGossip-BasedOur ApproachFeaturesConclusions

5. Motivation Reputation systems decompose into: Trust model. Data management scheme. Data management solutions: Central database: inappropriate. Previous suggestions plagued by: large data structures, evaluation of trust is based on local information. Reputation systems decompose into: Trust model. Data management scheme. Data management solutions: Central database: inappropriate. Previous suggestions plagued by: large data structures, evaluation of trust is based on local information. IntroductionGossip-BasedOur ApproachFeaturesConclusions

6. The Telephone Call Problem IntroductionGossip-BasedOur ApproachFeaturesConclusions

7. Computing Aggregate Info Push-Sum [Kempe et al. 2003] computes avg of values at nodes. At each turn, each node maintains sum and weight. Sends half of sum and weight to node chosen randomly. Current evaluation: sum/weight. The diffusion speed of uniform gossip U(n, ,  ) is an upper bound on the number of turns required so that the error at each node is at most  with probability 1- . Push-Sum [Kempe et al. 2003] computes avg of values at nodes. At each turn, each node maintains sum and weight. Sends half of sum and weight to node chosen randomly. Current evaluation: sum/weight. The diffusion speed of uniform gossip U(n, ,  ) is an upper bound on the number of turns required so that the error at each node is at most  with probability 1- . IntroductionGossip-BasedOur ApproachFeaturesConclusions

8. Computing Aggregate Info Theorem: U(n, ,  )=O( logn + log(1/  )+log(1/  )). Aggregation persists in face of failures. Still works when point-2-point communication cannot be assumed, e.g. in peer-2-peer networks. Theorem: U(n, ,  )=O( logn + log(1/  )+log(1/  )). Aggregation persists in face of failures. Still works when point-2-point communication cannot be assumed, e.g. in peer-2-peer networks. IntroductionGossip-BasedOur ApproachFeaturesConclusions

9. r 2 1  NA r 2 2  1 r 2 3  NA r 2 4  NA A demonstration 1 2 4 3 r 1 1  NA r 1 2  1 r 1 3  NA r 1 4  NA r 1 1  1 r 1 2  NA r 1 3  NA r 1 4  NA r 2 1  NA r 2 2  1 r 2 3  0.9 r 2 4  NA r 3 1  NA r 3 2  NA r 3 3  1 r 3 4  NA r 3 1  NA r 3 2  0.6 r 3 3  1 r 3 4  NA r 1 1  1 r 1 2  0.3 r 1 3  NA r 1 4  NA r 2 1  0.1 r 2 2  1 r 2 3  0.9 r 2 4  NA IntroductionGossip-BasedOur ApproachFeaturesConclusions Should I deal with 2?

10. Details of approach Each agent i maintains evaluation r i j of agents j it interacted with. Let r j =  k r k j. When interacting with j, i obtains r j using Push-Sum. Inputs are r k j. Salient features: Decentralization. Scalability. Robustness to failure. Globality. Simple data structures. Each agent i maintains evaluation r i j of agents j it interacted with. Let r j =  k r k j. When interacting with j, i obtains r j using Push-Sum. Inputs are r k j. Salient features: Decentralization. Scalability. Robustness to failure. Globality. Simple data structures. IntroductionGossip-BasedOur ApproachFeaturesConclusions

11. Motivates Truthfulness A priori, makes sense to be dishonest on occasion. Each agent has thresholds r i thr,  i. Must repeatedly decrease  until sure of result. Theorem: Let  ij =|r j -r i thr |. Then the time to decide is O( logn + log(1/  i ) + log(1/  ij )). Higher reputation  close deals faster. A priori, makes sense to be dishonest on occasion. Each agent has thresholds r i thr,  i. Must repeatedly decrease  until sure of result. Theorem: Let  ij =|r j -r i thr |. Then the time to decide is O( logn + log(1/  i ) + log(1/  ij )). Higher reputation  close deals faster. IntroductionGossip-BasedOur ApproachFeaturesConclusions

12. Impervious to attacks During Push-Sum, agents repeatedly update evaluation. Consider: i maintains sum/weight=1. Theorem: at each node, evaluation of average converges to 1 in probability. Theorem: after T stages, the expected difference in the average  T/2n. Insubstantial when T=O(logn). During Push-Sum, agents repeatedly update evaluation. Consider: i maintains sum/weight=1. Theorem: at each node, evaluation of average converges to 1 in probability. Theorem: after T stages, the expected difference in the average  T/2n. Insubstantial when T=O(logn). IntroductionGossip-BasedOur ApproachFeaturesConclusions

13. Proof Sketch w S w S S w w S w S w S w w S S + IntroductionGossip-BasedOur ApproachFeaturesConclusions

14. Proof Sketch The difference in total sum, in stage t, is at most the total weight sent to the manipulator. The expected weight sent to the manipulator at stage t is ½. Linearity of expectation  multiply by T. Divide by n to obtain difference in average. The difference in total sum, in stage t, is at most the total weight sent to the manipulator. The expected weight sent to the manipulator at stage t is ½. Linearity of expectation  multiply by T. Divide by n to obtain difference in average. IntroductionGossip-BasedOur ApproachFeaturesConclusions

15. Features: Decentralization. Scalability. Robustness to failure. Globality. Simple data structures. Motivates Truthfulness. Impervious to certain attacks. Some existing trust models are compatible [Aberer and Despotovic 2001, Xiong and Liu 2003]. Features: Decentralization. Scalability. Robustness to failure. Globality. Simple data structures. Motivates Truthfulness. Impervious to certain attacks. Some existing trust models are compatible [Aberer and Despotovic 2001, Xiong and Liu 2003]. IntroductionGossip-BasedOur ApproachFeaturesConclusions