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Enhanced Social Learning via Trust and Reputation Mechanisms in Multi-agent Systems PhD Completion Seminar Golriz Rezaei Supervisors: Dr. Michael Kirley.

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Presentation on theme: "Enhanced Social Learning via Trust and Reputation Mechanisms in Multi-agent Systems PhD Completion Seminar Golriz Rezaei Supervisors: Dr. Michael Kirley."— Presentation transcript:

1 Enhanced Social Learning via Trust and Reputation Mechanisms in Multi-agent Systems PhD Completion Seminar Golriz Rezaei Supervisors: Dr. Michael Kirley Dr. Shanika Karunasekera Dept. Computer Science and Software Engineering The University of Melbourne, Australia 20 April 2011

2 Outline Overview Motivation Enhanced Social Learning Research Goals / Questions / contributions / publications Background Trust and Reputation in Multi-agent Systems Trust and Reputation in Evolutionary Game Theory Evolutionary Games on Graphs The Research work First Model Second Model Third Model Concluding Discussion Acknowledgment and Questions?

3 Motivation Multi-agent Systems (MAS)? Interacting autonomous agents Different geographical locations Varying cognitive / processing abilities Limited information / partial knowledge Perform tasks  Receive utility Difficult tasks  Beyond individual agent capacity Maximise utility  Interact (collaboration / resource sharing) Problem? Appropriate partners  Successful performance  Maximise utility Open dynamic MAS  Uncertainty + Partial knowledge Establishing strategic connections is difficult!

4 Enhanced Social Learning Social Learning ( biological background )? Learning through observation / interaction with others Knowledge transmission without genetic materials Acquire knowledge from others without incurring the cost / time Major mechanism  Imitation (perceive and reproduce behaviour) Why good? keep track of beneficial interaction partners save time / energy / cost Improve long term performance (individual / system) Problem?  error-prone / outdated / inappropriate information

5 Solution?  selective When  High individual trial-and-error cost Intermediate environment change rate How  Mixed with personal innovation From whom  Agents are heterogeneous Appropriate role models  Important for performance Partner selection Enhanced Social Learning cont.

6 1)Top-down  Plan at design time Ability of the designer  predict optimal connections in advance Fixed structure of relations (random / particular topology) Autonomy condition + Environmental condition  not realistic 2)Automatic learning  Build and sustained adaptively at run time Trust & Reputation  Formal definition? Evaluate before interaction  Partner selection / Decision making Relations evolve  Partner’s reliability / trustworthiness Survey in Ch2 Enhanced Social Learning cont. Evolutionary game theoryConcrete App MAS

7 Coevolutionary Endogenous Social Networks Dynamic relation formation TopologyBehaviour Social ties Agents’ strategies

8 Proposed framework 1.Life-experiences 2.Endogenous Evolving Social Networks  Evaluation Trust & Reputation Social Learning Enhanced Social Learning 1) Social Dilemma  Evolutionary Games 2) Advice-seeking in Distributed Service Provision Applications ?

9 Research goals and questions Central hypothesis: “ Does incorporating concepts of trust and reputation within a social learning framework help to enhance the agents’ interactions in a MAS? And consequently does it help to improve their long term performance?” 1.(Life-experiences / Aging) + (Coevolutionary endogenous social networks) Trust / Reputation?  Effective social learning approaches? 2.Encourage cooperation in social dilemmas? Broader perspective of general MAS applications (Advice-Seeking for Resource Discovery in Distributed Service Provision) 3.Impacts of agents’ heterogeneity (behaviour/attributes/preferences) 4.Structural characteristics of the underlying evolved relationship networks? 5.Interaction patterns system's behaviour? Interaction patternSystem behaviour

10 Publications Life Experiences in Spatial 2-player Prisoners’ Dilemma Game 1.G. Rezaei and M. Kirley (2008). Heterogeneous payoffs and social diversity in the spatial prisoner's dilemma game. In X. Li, M. Kirley, and M. Zhang, editors, Proceedings of 7th International Conference on Simulated Evolution and Learning (SEAL), volume 5361 of Lecture Notes in Computer Science, pages , Springer. 2.G. Rezaei and M. Kirley (2009). The effects of time varying rewards on the evolution of cooperation. Evolutionary Intelligence, 2(4): First Model

11 Publications cont. N-player Prisoners' Dilemma Game on an Evolving Social Network 1.G. Rezaei, M. Kirley and J. Pfau (2009). Evolving cooperation in the N- player prisoner's dilemma: A social network model. In K. B. Korb, M. Randall, and T. Hendtlass, editors, Artificial Life: Borrowing from Biology (ACAL), volume 5865 of Lecture Notes in Computer Science, pages 32-42, Springer Verlag, Berlin. 2.An extended version is under preparation (2011). Distributed Advice-Seeking on an Evolving Social Network 1.G. Rezaei, J. Pfau and M. Kirley (2010). In Distributed Advice-Seeking on an Evolving Social Network IEEE/WIC/ACM International Conference on Intelligent Agent Technology. Second Model Third Model

12 Outline Overview Motivation Enhanced Social Learning Research Goals / Questions / contributions / publications Background Trust and Reputation in Multi-agent Systems Trust and Reputation in Evolutionary Game Theory Evolutionary Games on Graphs The Research work First Model Second Model Third Model Concluding Discussion Acknowledgment and Questions?

13 Trust: [Gambetta 1988] Subjective probability expects performs a given action  welfare depends on. Reputation: Information about an agent’s behavioural history. [Ismail et. al. 2007]  Challenging  Confusing  Inconsistent Typology  Background Trust and Reputation in MAS ABA Survey in Ch2

14 Background cont. Typology Suitable mechanisms 1) Variety of sources of information 2) Individuals/distributed evaluation 3) Robust against possible lying/fraud

15 Game Theory (GT)? Evolutionary GT? Social Dilemmas? “Cooperation”  “Tragedy of the commons” Autonomous individuals  Theory  individuals behave selfishly  Nature  cooperation exists  Biology, Economics, Sociology  ( IEEE Trans, Statistical Physics, Nature, CEC, GECCO … )  Distributed systems (P2P) (DAI)  Crucial for performance of MAS Abstract framework  many real-life scenarios Simple games + rich dynamics  Appropriate mathematical tools  Study complex Strategic interactive scenarios act cooperatively  contribute to the social welfare behave selfishly (not investing anything )  enjoy the free benefits shared among all the members (free-riding)  Mechanisms? Background cont. Evolutionary Games Still an open ended question! (AAMAS) [Hardin 1968]

16 Why?  The most difficult settings for cooperation  Robust and fundamental method of modelling  Simplicity of statement and design MAS (2-PD)  2 players / agents  2 choices (C or D)  Payoff joint actions  Actual values  order Order change  game change i) T > R > P > S ii) 2R >= (T + S) (D,D)  Nash Equilibrium Background cont. Prisoners’ Dilemma

17 Trust and Reputation in Evolutionary Games 5 Fundamental mechanisms  Evolution of “Cooperation”  Kin selection vs. Group selection  Direct Reciprocity -Iterated encounters -Return of altruistic act / punishment - “You scratch my back, I’ll scratch yours!”  Indirect Reciprocity -Unlikely repeated interactions -Return from third parties -Image/Reputation score - “You scratch his back, I'll scratch yours!”  Network Reciprocity -Social / spatial constraints  Non-uniform / Local neighbourhood interactions -Clustering effect (community structure)  Enhances cooperation [Nowak 2006] Compare  Trust & Reputation

18 Background cont. Basics of the Networks Network graph, G(N, E), N finite set of nodes (vertices) E finite set of edges (links) G represented by N×N adjacency matrix a ij = 1 there is an edge between node i and j a ij = 0 otherwise A graph with 8 vertices and 10 edges Network of computers

19 Background cont. Topological properties Degree, k i, of a node Path length, L average separation between any two nodes Clustering coefficient, C i, of a node probability that two nearest neighbours of a node are also nearest neighbours of each other.

20 Background cont. Types of Networks Random  uniform probability p Mathematical objects  Comparison only (not good for real social network) Regular  Not good for real networks Small-World  Regular lattice Random graph One end of each link  rewired small probability p Highly clustered + Short path length Scale-Free Grow  preferential attachment Power-law degree distribution Most nodes very few links, small nodes highly connected 1-D circular 2-D square grid (lattice) transition 0  p  1 ? Small-world graph The same degree

21 Background cont. Evolutionary Games on Graphs Local neighbourhood interaction Population Structure  system dynamics Clusters of cooperators  Enhance cooperation Developmental stages -scaffolding interaction  different types of network topology -parameters ( magnitude rewards/punishments, population size, initial condition, update rules ) -mathematical analysis difficult  Computational simulations Non-uniform interactions Static Networks Socio-biological Uniform interactions Non-uniform interactions Dynamic Networks 2-D Grids Realistic Social Net

22 Outline Overview Motivation Enhanced Social Learning Research Goals / Questions / contributions / publications Background Trust and Reputation in Multi-agent Systems Trust and Reputation in Evolutionary Game Theory Evolutionary Games on Graphs The Research work First Model Second Model Third Model Concluding Discussion Acknowledgment and Questions?

23 Only Decision making No Partner selection Cooperative behaviour First Model Life Experiences in Spatial 2-PD Game Trust & Reputation Social Learning Enhanced Social Learning Life-experiences & Age Fixed Network (grid)  Local neighbourhood interaction  Moore  Accumulates received payoffs  Fitness  End of each round  Imitate the most successful neighbour (MSN)  Clusters of cooperators  outweigh losses against defectors ?

24 First Model cont. The challenge Typically  “Universal fixed payoff matrix” Hypothesis  Introducing “social diversity” alters trajectory of the population  Adaptive rewards  (I ndividual agent strategies + Life-experiences) Given a limited agent life span  MSN  ( Highest accumulated normalized utility + Older) Role model trustworthiness! Age  α i (t+1) = α i (t) + 1 Life-span  λ i randomly from a uniform distribution [min, max] (αi(t) == λi  dies and replaced by a new random agent) Personal version of payoff matrix  updated at each time step based on experience level Each agent Update rule Contributions ?

25 First Model cont. Adaptive rewards Update  Where is the payoff values for agent i at time t is the default payoff matrix values T, R, P, S is the magnitude of the rescaled values is the age of agent i at time t is the expected life time of agent i is limiting factor and characterises the uncertainty related to the environment 1) 2)

26 First Model cont. Scenarios 1.Standard PD  Universal fixed Payoffs + Age 2.Homogeneous model  Universal fixed Payoffs+Age 3.Heterogeneous model  Individual Adaptive Payoffs + Age (3 versions: update 4 elements / update 1 element / update 1 element capped)  What is the equilibrium state?  Coevolution  Altruistic behaviour + Non-stationary dynamic rewards (Het 1)(Het 2)(Het 3) (HOM) (S)

27 First Model cont. Experimental setup 2-D grid (32*32)  Implemented in Netlogo 4.0 [Wilensky 2002] Population initialization  (20% C – 80% D) / (50% C – 50% D) Payoff (small: T=1, R=1, P=0, S=0) / (Big: T=5, R=3, P=1, S=0) Life-span distributions (λ i )  [0,50] / [0,100] / [50,100] Environmental constraint K  [0.1 : : 0.2] Each trial  iterations & All configurations  30 times Statistical results are reported

28 First Model cont. Sensitivity to the base payoff values Payoff (small: T=1, R=1, P=0, S=0) / (Big: T=5, R=3, P=1, S=0) StandardHomogeneous (HOM)(S)

29 First Model cont. Heterogeneous vs. Homogeneous Payoff: (Big: T=5, R=3, P=1, S=0) / Population initialization (20% C – 80% D)(50% C – 50% D)

30 First Model cont. Snapshots Payoff: (Big: T=5, R=3, P=1, S=0) / Population initialization (20%C – 80% D) (Het 1) (Het 2) (Het 3) (HOM) Varying size clusters of cooperators (black) Other extra results for different parameters K, life-span, replacement …

31 Outline Overview Motivation Enhanced Social Learning Research Goals / Questions / contributions / publications Background Trust and Reputation in Multi-agent Systems Trust and Reputation in Evolutionary Game Theory Evolutionary Games on Graphs The Research work First Model Second Model Third Model Concluding Discussion Acknowledgment and Questions?

32 Decision making Partner selection Coevolution  (Interaction network + Individuals’ strategy) Second Model N-PD on an Evolving Social Network Trust & Reputation Social Learning Enhanced Social Learning Endogenous Evolving Social Networks  2-PD  N-PD Cooperative behaviour in larger groups  More difficult ! (N > 2) Real-world social communities  Fixed underlying network  Relaxed Relations evolve over time Link weights  Trust & Reputation

33 Natural extension of 2-PD Utility  [Boyd and Richerson 1988] Conditions Second Model cont. N-player Prisoners’ Dilemma defection is preferred for individuals contribution to social welfare is beneficial for the group Conventional EG (D,D, … all D)

34 Agents play cooperatively  form social links (reinforced) One agent defects  breaks his links with the opponents Second Model cont. Evolving Relations slow positive / fast negative

35 Incorporating “social network” into N-player PD  Network evolves by cooperative behaviour Introducing “cognitive” agents  Decision making based on some function of the opponents Second Model cont. Contribution - Hypothesis Encourage high levels of cooperation Persist for longer Analyse the state of the underlying network

36 Second Model cont. Schematic Algorithm Algorithm: Social network based N-PD model Require: Population of agents P, iteration = i max, players N 2 1: for i = 0 to i max do 2: G = 0; 3: while g = NextGame(P,G, N) do 4: G = G {g} 5: PlayGame(g) 6: AdaptLinks(g) 7: end while 8: a,b = Random Sample(P) 9: CompareUtilityAndSelect(a,b) 10: end for Decision making Partner selection

37 First agent  Randomly from remaining population Two Scenarios (N-1) partners Second Model cont. Game Formation Partner selection Randomly from remaining population From the first agent remaining social contacts probabilistically

38 Two scenarios (cognitive abilities) Pure strategy  (always cooperate/defect) Mixed strategy  (play probabilistically) Discriminators  function of Agents receive corresponding payoff based on outcomes (Boyd and Richerson function) Second Model cont. Game Execution Decision making generosity gradient Average links weight

39 Second Model cont. Snapshots |P| = 25, N = 3, Defector, Cooperator, Discriminator Self-organize social ties based on their self-interest Strategy update cultural evolution

40 Second Model cont. Scenarios   Partner selection + Decision making (Random matching) (Pure strategy)   Partner selection + Decision making (Social Network game formation) (Pure strategy)   Partner selection + Decision making (Random matching) (Pure strategy + Discriminators)   Partner selection + Decision making (Social Network game formation) (Pure strategy + Discriminators) Step 1 Step 2 Step 3 Step 4

41 Population size = 1000 Group sizes = (2, 4, 5, 10, 15, 20) ε = 0.9  Game formation probability b = 5 and c = 3 (payoff values benefit & cost) Pure strategy scenario (50% pure C – 50% pure D) Mixed strategy scenario (33.3% each) α = 1.5 and β = 0.1 (decision function) average 20 independent trials up to iterations Second Model cont. Experimental Setup What is the equilibrium state and network topology?

42 Second Model cont. Group size vs. Strategy Step 1Step 2 Step 3Step 4

43 Second Model cont. Emergent Social Networks Clustering Coefficient Step 2 Step 3 Step 4

44 Second Model cont. Final Degree Distribution Step 4 N=2 Step 4 N=5 Cooperation higher  degree distribution higher Size & shape  depend on N

45 Outline Overview Motivation Enhanced Social Learning Research Goals / Questions / contributions / publications Background Trust and Reputation in Multi-agent Systems Trust and Reputation in Evolutionary Game Theory Evolutionary Games on Graphs The Research work First Model Second Model Third Model Concluding Discussion Acknowledgment and Questions?

46 Decision making Partner selection Coevolution  (Interaction network + System’s behaviour) Third Model Distributed Advice-Seeking on an Evolving Social Network Trust & Reputation Social Learning Enhanced Social Learning Endogenous Evolving Social Networks Life-experiences  Games  Advice-Seeking in Distributed Service Provision  Relations evolve over time ( Link weights  Trust & Reputation ) ?

47 Third Model cont. Distributed Infrastructure Technology Characteristics 1)Unknown large environment 2)Varieties of selection options 3)Users are heterogeneous 4)Exact characteristics not available until accessed, if it is made explicit at all Ex./ Specialized protein search engines, Netflix Approaches 1) Individual try & error 2) Central registration directory (Brokers, Web Service [Facciorusso et. al. 2003] ) 3) Advice seeking Direct exchange of “selection advice” beneficial! ex./ Learning [Nunes and Oliveira 2003 ], Distributed Recommender Systems Question?

48 Social Networks! Third Model cont. Advice-Seeking Question: Heterogeneous individual requirements Whom? Challenge: Identify other suitable users difficult! - Large number of them - Preferences not publicly available - Not in a position to make their own preferences explicit Social contacts serve as valuable resources Manage improve long term payoff gains

49 Third Model cont. Abstract Framework Agent-based simulation (resources + agents) Repeatedly Subjective Utility Goal = M aximize long term utility, limited selections Challenge = Identify appropriate resources Evolving Social Network - Connect with similar minded  Autonomously based on local information only - Receive advice  improve resource selection - Learn their own subjective utility  advice accuracy decide retain / drop the contact - Form new connections  Seek referrals Match?

50 Third Model cont. What we study? This capability Connection network Advice exchange Agents’ interactions Social relationships The evolving social network Utility gain Affect the match? How co-evolve? Improve? Change?

51 Algorithm: Evolving Social Network Advice seeking Require: Population of agents, set of resources, rounds, evolutionary rate, maximum out degree, recommendation threshold t, default edge weight 1: Weighted Graph = InitializeGraph (,, ) 2: for r = 1 to do 3: for each a ∈ in random order do 4: 5:if Random() > then 6:AccessResource(a, ) 7:else 8:Query (a,,, t) 9:end if 10:if Random() < then 11:AdaptLinks(a,, RANDOM() <, ) 12:end if Third Model cont. Schematic Algorithm 1-Initialization 2-Exploitation/Exploration 3-Advice selection 4-Assessment * 5-Network Adaptation *

52 Third Model cont. 1-Initialization Heterogeneous pool of resources n-dimensional binary feature vector f r initialized randomly Heterogeneous agent population n-dimensional binary preference vector p a initialized randomly Initialize Graph(,, ) 2 scenarios:  random agents no structural restriction  social agents outgoing edges, default weight ( = 0.5)

53 Selection based on personal knowledge / Query others! Probabilistic Quality of the agent’s acquired knowledge Exploit Access the largest utility resource it knows so far Explore Seek advice (resource, utility) Random agents other random agents Social agents outgoing edges, social contacts Third Model cont. 2-Exploitation/Exploration

54 Third Model cont. A suggestion probabilistically 1.Advisor Link’s weight 2.One of his suggestions Reported utility Subjective utility of accessed resource Similarity between p a & f r Normalized Hamming distance mapped to [-1,1] Positive values better than average random selection Negative values random selection would have done better 3-Advice selection

55 Third Model cont. Social agents learn from their interactions adjust the weight of links Following a particular suggestion - Positive | u a (r) – u rep (r)| < thr dis - N egative Adjust the link weight with multiple advisors - the link weight - w(a,b) < thr tolerance remove the edge, free slot! 4-Assessment *

56 Third Model cont. Social agents opportunity to change their links probabilistically! Link to a random agent with default weight Ask for referrals Trust propagation [Massa and Avesani 2007, Vidal 2005] 5-Network Adaptation *

57 Third Model cont. Snapshots  Steps 4 & 5 eventually make link with similar preferences  Similar-minded community spot beneficial resources faster

58 Third Model cont. Experimental Setup Monte-Carlo simulations, various parameter settings Scenarios (Social agents only and Random agents only) Population sizes (small = 100, large = 300 agents) Environmental complexity  |R| = (1000, 5000, 10000, 50000) Heterogeneity  |p a | & |f r | = (2, 3, 4, and 5) First 1000 iterations  Average over 30 independent trials (Note! exhaustive exploration will find eventually)

59 Third Model cont. Basic Model behaviour Social agents gain higher utilities? (|A| = 100, |p a | & |f r | = 3, |R| = 5000)

60 Third Model cont. Environmental Complexity Efficiency of social and random scenarios Facing more complex environments? |A| = 100 |p a | & |f r | = 3 |R| = (1000,5000,10000,50000)

61 Third Model cont. Analysis the underlying Network |A| = (100, 300) / |R| = 5000 / |p a | & |f r | = (2, 3, 4, 5)  Modularity Score Small population Large population

62 Outline Overview Motivation Enhanced Social Learning Research Goals / Questions / contributions / publications Background Trust and Reputation in Multi-agent Systems Trust and Reputation in Evolutionary Game Theory Evolutionary Games on Graphs The Research work First Model Second Model Third Model Concluding Discussion Acknowledgment and Questions?

63 Efficacy of Enhanced Social learning approaches  Agents interactions  Individuals’ and System’s long term (utility) performance Life-experiences + Endogenous Evolving Social Networks  Trust and Reputation  ESL First Model (2-PD on Fix Grid Structure) : Adaptive rewards  Life-experiences / Age Innovative notion of role model trustworthiness / Heterogeneous social diversity  Cooperation Second Model (N-PD on an Evolving Social Network) : Endogenous network formation  Partner selection + Decision making  (Cooperation) Emergent Social Networks  High average clustering + Broad-Scale heterogeneity Third Model (Distributed Advice-Seeking for Resource Discovery) : Life-experiences + Endogenous network formation  Similar minded (appropriate role models) Strongly connected communities with similar preferences  Higher utility Summary Thesis contributions

64 Limitations Generality of Adaptive rewards on Fixed interaction networks 2-PD on simple Grid  Other classes of games (Hawk-Dove / Stag-Hunt / …) Age attribute  Heterogeneity  Other concepts?  How encourage Cooperation? Simple Grid  Other fixed topologies?  Effect of different neighbourhood structures Generality of Adaptive rewards on Evolving Social Networks Dynamic Payoffs  N-PD framework  Not satisfying! (limited parameter settings) Extensive analysis  Determine why it was not helpful / If it is helpful at all / How? (Ex./ Bigger ranges of life-span / different time scales for update rules + evolution interaction network) Realistic approaches for Advice-Seeking framework Generic model  Inspired by several distributed service provision systems Synthetic date  Set up specific, controlled platform  Represent semi-realistic MAS  Evaluate performance of the ESL  Not solution for particular application! Exploit such techniques  real technological systems  real data sets  real users preference profiles  binary preferences  Not realistic! Dynamic Environment  Dynamic relations / Users / Preferences / Resources ?

65 Future work N-PD  fixed group sizes + similar for all agents Dynamic group formation + heterogeneous sizes  different communities in real-world Advice-Seeking model  similarities with Recommender Systems Different purpose here  BUT! Interesting to Modify and apply in such context  Comparison with other models Enhanced Social Learning  Imitation (basic cultural learning) Extend to other methods of MAS learning  ex./ Reinforcement Learning Evolutionary Game Theory + Advice-Seeking  Investigation domains Potential domains (MAS)  P2P / Mobile Ad-hoc Networks / Grid Computing Robustness of the proposed mechanisms Different scales of dynamicity in real-world environment

66 Acknowledgment 1.Michael, Shanika, Adrian 2.Jens 3.Les, Ed, Leon, Liz, … 4.Agent lab members, Rebecca, … 5.Dept. Computer Sci / Uni Melb 6.Rahil, Leila, Parvin, Toktam, … 7.Lab colleagues (Saeed/Raymond/…) 8.…

67 Questions? Thank you

68 References 1)D. Gambetta. Can We Trust Trust? In D. Gambetta, editor, Trust: Making and Breaking Cooperative Relations, pages Basil Blackwell, )R. Ismail, A. Jøsang, and C. Boyd. A survey of trust and reputation systems for online service provision. Decision Support Systems, 43:618644, )M. A. Nowak. Five rules for the evolution of cooperation. Science, 314: , )R. Boyd and P. Richerson. The evolution of reciprocity in sizeable groups. Journal of Theoretical Biology, 132: , )C. Facciorusso, S. Field, R. Hauser, Y. Hoffner, R. Humbel, R. Pawlitzek, W. Rjaibi, and C. Siminitz. A Web Services Matchmaking Engine for Web Services. In E-Commerce and Web Technologies, Lecture Notes in Computer Science, pages , )L. Nunes and E. Oliveira. Advice-exchange in heterogeneous groups of learning agents. In Proceedings of the second international joint conference on Autonomous agents and multiagent systems, pages , )P. Massa and P. Avesani. Trust-aware recommender systems. In Proceedings of the 2007 ACM conference on Recommender systems, pages , )J. M. Vidal. A Protocol for a Distributed Recommender System. In J. Sabater R. Falcone, S. Barber and M. Singh, editors, Trusting Agents for Trusting Electronic Societies. Springer, )G. Hardin. The Tragedy of the Commons. Science, 162:1243{1248, )U. Wilensky. Modelling Nature's Emergent Patterns with Multi-agent Languages. In Proceedings of EuroLogo, NetLogo is a cross-platform multi-agent programmable modelling environment. See

69 Backup Slides

70 First Model cont. Sensitivity to the magnitude of K Payoff: (Big: T=5, R=3, P=1, S=0) / Population initialization (20%C – 80% D) (Het 1) 1) 2)

71 First Model cont. Sensitivity to the Life-span ( λ i ) Payoff: (Big: T=5, R=3, P=1, S=0) / Population initialization (20%C – 80% D) (Het 1)

72 First Model cont. Sensitivity to the replacement strategy Payoff: (Big: T=5, R=3, P=1, S=0) / Population initialization (20%C – 80% D) (Het 1)

73 Third Model cont. Metrics Average utility Average error rate Efficiency

74 Third Model cont. The influence of Heterogeneity Finding similar-minded agents important role How heterogeneity in |p a | & |f r | affect the performance of social agents? |A| = (100, 300) |R| = 5000 |p a | & |f r | = (2, 3, 4, 5) T = 1000 Averaged accumulated utility


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