Collective Behavior in Multi-Agent Systems. Zhangang Han zhan@bnu.edu.cn Summer School School of Systems Science Beijing Normal University July 08, 2013. Complexity Feature. Definition of Complexity Research varies Features Many elements interact in a system Nonlinear
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Complexity Feature • Definition of Complexity Research varies • Features • Many elements interact in a system • Nonlinear • Heterogeneous vs. Homogeneous • Cooperation vs. competition • Overall considerations • Symmetry breaking • Decision making facing ever changing environment
Former Yugoslavia Fig. 2. (A) Census data from 1991 shown here in map form were converted into a spatial representation and used in an agent-based simulation shown in (B).
India Fig. 3. (A and B) Spatial representation of Indian census data from 2001 of six indicated groups was converted into an agent-based simulation shown in (C). Our prediction of conflict-prone areas [red areas in (D)] agrees with states where major ethnic violence has been reported [red areas in (E)] between 1999 and 2002, with the red shading intensity corresponding to the rank order of states by number of incidents.
Stick pulling experiment • Ling Li, Alcherio Martinoli, and Yaser S. Abu-Mostafa, Emergent Specialization in Swarm Systems, H. Yin et al. (Eds.): IDEAL 2002, LNCS 2412, pp. 261–266. • Martinoli, A., Mondada, F.: Collective and cooperative group behaviours: Biologically inspired experiments in robotics. In Khatib, O., Salisbury, J.K., eds.: Proceedings of the Fourth International Symposium on Experimental Robotics (1995). Lecture Notes in Control and Information Sciences, Vol. 223. Springer-Verlag, Berlin (1997) 3–10
Flocking with Confrontation Vicsek model (Vicsek T, PRL, 1995) • The only rule of the model is at each time step a given particle driven with a constant absolute velocity assumes that average direction of motion of the particles in its neighborhood of radius r with some random perturbation added.
Flocking with Confrontation Social force model for pedestrian dynamics (Helbing D., Molnar P., Phys Rev E, 1995) Simulating dynamical features of escape panic. (Helbing D., Farkas I., Vicsek T, Nature, 2000)
Effective leadership and decision making in animal groups on the move，I. D. Couzin, Nature, 2005. Interaction & information It may be unreasonable to assume that group members have the capacity for individual recognition. • Asumptions: • the absence of complex signalling mechanisms • not possible for group members to establish who has and has not got information • Questions: • How information about the location of resources, or of a migration route, can be transferred within groups; • How individuals can achieve a consensus when informed individuals differ in their preferences;
In a given time step, informed individuals find themselves moving in a similar direction (here within a 20-degree arc) to their preferred direction, w is reinforced (by winc, up to a maximum, wmax), otherwise it is reduced (by wdec, to a minimum of 0) w, wmax= 0.4 n1 = 6, n2 = 5 n1 = 5, n2 = 5 n1 = 6, n2 = 4 winc =0.012 wmax= 0.0008 n1 = 5, n2 = 5 n1 = 6, n2 = 5 n1 = 6, n2 = 4 winc =0.012 wmax= 0.0008 w-> w:winc :wmax or w-> w:-wdec :0 n1 = 11, n2 = 10 n1 = 10, n2 = 10 n1 = 11, n2 = 9
The Problem • P. Krugman studied the role of geography in economic development • Argued that the role of geography should have become a mainstream concern within economics long ago. 1. Krugman P (1999) The role of geography in development. International regional science review 22: 142.
Previous studies believe that economies benefit from specific geographic advantages such as coastlines and areas connected to the coast by navigable rivers, which are more densely populated than hinterlands • Krugman noted that small random historical events may have large consequences for economic geography, and these two approaches are complementary, rather than contradictory.
Idea of the current study • We use agent-based computational experiments. We hypothesize that a key factor may be the information sharing mechanism.
we examine three levels of information sharing: • 1) no information sharing • 2) friend information-sharing (within a community) • 3) pheromone information-sharing, which are analogous to pheromones in the biological world. • The spectrum in the present study spans from no information sharing to a point just shy of global information sharing. This spectrum enables us to assess the extent to which the information sharing mechanism alone contributes to the aggregation of economic activities. • The extent of information sharing serves as an “order parameter,”
Stylized fact explained • The results show that market size exhibits a power-law distribution for the pheromone information-sharing mechanism and an exponential distribution for each of the other two information-sharing mechanisms. • Power-law distributions have been observed in a diverse range of fields, including biology, economics, sociology, engineering and physics. Several well-known examples of phenomena that exhibit ”scaling” behavior are city sizes [22], firm sizes [23], 22. Gabaix X (1999) Zipf's law for cities: an explanation. The Quarterly Journal of Economics 114: 739-767. 23. Axtell RL (2001) Zipf distribution of US firm sizes. Science 293: 1818-1820.
Conclusions:Path Dependence, Positive Feedback -> Symmetry Breaking (Brian Arthur, 1999, Science) • 1. This paper provides an alternative approach to study the geographic aspects of economic development based on Krugman’s model. • 2. The agent-based model provides us a test bed to test which information-sharing mechanism is proper to describe the real economic system. • 3. This is the first work as far as we know that studies the contribution of information-sharing alone to the spatial structure of an economic system. • 4. The power-law distribution of market size corresponds to the stylized fact of city size and firm size distributions. • 5. The symmetry breaking process from a homogeneous initial state to a heterogeneous spatial structure is demonstrated.
A Trust and Reputation Model Considering Overall Peer Consulting Distribution • Heterogeneous vs. Homogeneous • Overall Consideration • In new, widespread peer-to-peer (P2P) systems, peers are exposed to great risk due to frequent trading with unfamiliar peers. • many studies are devoted to trust and reputation mechanisms in P2P systems
Trust and reputation models • Notions: • Trust • Trust is the extent to which one party is willing to depend on something or somebody in a given situation with a feeling of relative security, even though negative consequences are possible. • Reputation • Overall quality or character as seen or judged by people ingeneral. • Relationship: • “There can of course be trust systems that incorporate elements of reputation systems and vice versa.” • Jøsang et al.
Classification of Models • Categorization: • Centralized/distributed • where to store the data. • Complete information/local information • how to utilize the data. • Ours is a distributed and local informationmodel.
Overall Consideration • The real connection between peers in the network has been found to be a scale-free connection
Comparison between models • Difference between the QoS and feedback(diff) of this work compared with the model of Yu et al..
Conclusion Results show that with the overall consideration, the model can maintain a low diff value (difference between QoS and feedback) while distinguishing the malicious peers even when the exaggeration coefficient is high.
Survival of an evasive prey • G. Oshanina,b,1, O. Vasilyevc,d, P. L. Krapivskye, and J. Klafterf,g • 13696–13701 PNAS August 18, 2009 vol. 106 no. 33 • studies the survival of a prey that is hunted by N predators • Pursuit-and-evasion problems have a long and fascinating history (1). The classical setup involves 2 agents—say, a merchant vessel pursued by a pirate ship that it desperately tries to evade.
Evasive Prey Model lnPev(t) ∼ (N/V)2lnPimm(t) Pimm(t)=e-aS(t) Pimm(t)=e-a3S(t) r=1 =N/V
MODEL(CONT.) PREDATORS HOP(FIG.A) PREYS HOP(FIG.B) 35 2014/9/25 • Find a nearest prey • Choose a direction, the next position is one-step far site on the direction. • Hop with two case below: • If the position occupied by another predator, hopping predator will be blocked and wait for next turn. • If the position occupied by prey, the prey will be caught and moved out of the Lattice • Find a nearest prey • Choose a direction, the next position is one-step far site on the direction. • Hop with a case below • If the position occupied by another prey or a predator, the hopping prey will be blocked and wait for next turn. BNU System Department
AGGREGATION STRATEGY 36 2014/9/25 • When the preys are escaping, they may tend to aggregate as a group to increasing the survival efficiency. • Escape with aggregation strategies or not under a probability • The aggregation tendency: p • Confirm the directions away from its nearest predator • Calculate the aggregation point • Find the nearest site to the aggregation point within next step among the directions(Euclidean distance) BNU System Department
RESULT 37 2014/9/25 Impact on survival time distribution BNU System Department
RESULT Aggregation to the average vector of coordinates Aggregation to the nearest mate Aggregation to all the mates 38 2014/9/25 2014/9/25 Impact on the phase transition BNU System Department
Panic Crowd stampedes occur many times A short list (but not all) of significant crowd related disasters.
Helbing build the social force model (1995 PRE, 2000 Nature) • A widely applied approach to model pedestrians. Based on the social force model: • Helbing(2002) and Escobar(2003) show that it is possible to increase the outflow of crowd by suitably placing a pillar in front of the exit. • Helbing(2007) and Shukla (2009) used a genetic algorithm to optimize the design of the obstacles.
The Problem Different design of obstacles, pillar is good but the position is important. (Escobar 2003) A design of genetic algorithm, complex and has an unused part of the obstacle. ( Helbing 2007)
The Problem We consider the evacuation of a room of size 15m × 15m having a single exit of width 1m. This might be a public hall or inside a temple for example. We assume that there are 200 people in this room and due to some reason they all need to be evacuated. The room architecture is shown in the left figure. The same figure also shows the clogging of pedestrians near the exit. The figure is for = 5.0 m/s, i.e., when pedestrians are nervous and are in a hurry to leave the room.
