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

Outline Overview Background The Research work Concluding Discussion 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?

Motivation Multi-agent Systems (MAS)? Perform tasks  Receive utility 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!

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  error-prone / outdated / inappropriate information

Enhanced Social Learning cont. 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. 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 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 Evolutionary game theory Concrete App MAS

Coevolutionary Endogenous Social Networks Dynamic relation formation Social ties Agents’ strategies Topology Behaviour

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

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?” (Life-experiences / Aging) + (Coevolutionary endogenous social networks) Trust / Reputation?  Effective social learning approaches? Encourage cooperation in social dilemmas? Broader perspective of general MAS applications (Advice-Seeking for Resource Discovery in Distributed Service Provision) Impacts of agents’ heterogeneity (behaviour/attributes/preferences) Structural characteristics of the underlying evolved relationship networks? Interaction patterns system's behaviour? Interaction pattern System behaviour

Life Experiences in Spatial 2-player Prisoners’ Dilemma Game Publications Life Experiences in Spatial 2-player Prisoners’ Dilemma Game 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 585--594, Springer. G. Rezaei and M. Kirley (2009). The effects of time varying rewards on the evolution of cooperation. Evolutionary Intelligence, 2(4):207-218. First Model

Publications cont. N-player Prisoners' Dilemma Game on an Evolving Social Network 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. An extended version is under preparation (2011). Distributed Advice-Seeking on an Evolving Social Network G. Rezaei, J. Pfau and M. Kirley (2010). In Distributed Advice-Seeking on an Evolving Social Network. 2010 IEEE/WIC/ACM International Conference on Intelligent Agent Technology. Second Model Third Model

Outline Overview Background The Research work Concluding Discussion 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? 12

Background Trust and Reputation in MAS 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  A B A Survey in Ch2 13

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

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

Background cont. Prisoners’ Dilemma Why? (2-PD) 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 (D,D)  Nash Equilibrium i) T > R > P > S ii) 2R >= (T + S)

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

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 aij = 1 there is an edge between node i and j aij = 0 otherwise A graph with 8 vertices and 10 edges Network of computers

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

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 ? The same degree transition 1-D circular 2-D square grid (lattice) 0  p  1 Small-world graph

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 Socio-biological Uniform interactions Non-uniform interactions Dynamic Networks Non-uniform interactions Static Networks Realistic Social Net 2-D Grids

Outline Overview Background The Research work Concluding Discussion 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? 22

First Model Life Experiences in Spatial 2-PD Game Only Decision making No Partner selection Cooperative behaviour Trust & Reputation Social Learning Enhanced Social Learning Life-experiences & Age Fixed Network (grid) ? 1 2 3 4 5 6 7 8 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

First Model cont. The challenge Typically  “Universal fixed payoff matrix” Hypothesis  Introducing “social diversity” alters trajectory of the population Adaptive rewards  (Individual agent strategies + Life-experiences) Given a limited agent life span MSN  (Highest accumulated normalized utility + Older) Role model trustworthiness! Age  αi(t+1) = αi(t) + 1 Life-span  λi 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 Contributions ? Update rule

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)

First Model cont. Scenarios Standard PD  Universal fixed Payoffs + Age Homogeneous model Universal fixed Payoffs+Age 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 (S)  (HOM)  (Het 1) (Het 2) (Het 3)

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 (λi )  [0,50] / [0,100] / [50,100] Environmental constraint K  [0.1 : 0.025 : 0.2] Each trial  10000 iterations & All configurations  30 times Statistical results are reported

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) Standard (S) Homogeneous (HOM)

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)

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

Outline Overview Background The Research work Concluding Discussion 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? 31

Second Model N-PD on an Evolving Social Network Decision making Partner selection Coevolution  (Interaction network + Individuals’ strategy) 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 Trust & Reputation Social Learning Enhanced Social Learning Endogenous Evolving Social Networks

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

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

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

Second Model cont. Schematic Algorithm Algorithm: Social network based N-PD model Require: Population of agents P, iteration = imax, players N 2 1: for i = 0 to imax 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 Partner selection Decision making

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

Second Model cont. Game Execution Decision making 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) gradient generosity Average links weight

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

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

Second Model cont. Experimental Setup 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 40000 iterations What is the equilibrium state and network topology?

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

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

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

Outline Overview Background The Research work Concluding Discussion 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? 45

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

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

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 Networks! Social contacts serve as valuable resources Manage improve long term payoff gains

Third Model cont. Abstract Framework Agent-based simulation (resources + agents) Repeatedly Subjective Utility Goal = Maximize 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?

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? Change? Improve?

Third Model cont. Schematic Algorithm 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 1-Initialization 2-Exploitation/Exploration 3-Advice selection 4-Assessment * 5-Network Adaptation *

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

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

Third Model cont. - Positive | ua (r) – urep (r)| < thrdis 4-Assessment * Social agents learn from their interactions adjust the weight of links Following a particular suggestion - Positive | ua (r) – urep (r)| < thrdis - Negative Adjust the link weight with multiple advisors - the link weight - w(a,b) < thrtolerance remove the edge, free slot!

Third Model cont. opportunity to change their links probabilistically! 5-Network Adaptation * 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]

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

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  |pa| & |fr| = (2, 3, 4, and 5) First 1000 iterations  Average over 30 independent trials (Note! exhaustive exploration will find eventually)

Third Model cont. Basic Model behaviour Social agents gain higher utilities? (|A| = 100, |pa| & |fr| = 3, |R| = 5000)

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

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

Outline Overview Background The Research work Concluding Discussion 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? 62

Summary Thesis contributions 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

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? 

Future work Robustness of the proposed mechanisms 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

Acknowledgment Michael, Shanika, Adrian Jens Les, Ed, Leon, Liz, … Agent lab members, Rebecca, … Dept. Computer Sci / Uni Melb Rahil, Leila, Parvin, Toktam, … Lab colleagues (Saeed/Raymond/…) …

Questions? Thank you

References D. Gambetta. Can We Trust Trust? In D. Gambetta, editor, Trust: Making and Breaking Cooperative Relations, pages 213--237. Basil Blackwell, 1988. R. Ismail, A. Jøsang, and C. Boyd. A survey of trust and reputation systems for online service provision. Decision Support Systems, 43:618644, 2007. M. A. Nowak. Five rules for the evolution of cooperation. Science, 314:1560-1563, 2006. R. Boyd and P. Richerson. The evolution of reciprocity in sizeable groups. Journal of Theoretical Biology, 132:337--356, 1988. 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 37--49, 2003. 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 1084--1085, 2003. P. Massa and P. Avesani. Trust-aware recommender systems. In Proceedings of the 2007 ACM conference on Recommender systems, pages 17--24, 2007. 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, 2005. G. Hardin. The Tragedy of the Commons. Science, 162:1243{1248, 1968. U. Wilensky. Modelling Nature's Emergent Patterns with Multi-agent Languages. In Proceedings of EuroLogo, 2002. NetLogo is a cross-platform multi-agent programmable modelling environment. See http://ccl.northwestern.edu/netlogo/.

Backup Slides

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) 1) 2) (Het 1)

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

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)

Third Model cont. Metrics Average utility Average error rate Efficiency

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