RePast Tutorial II Prof. Lars-Erik Cederman Center for Comparative - - PowerPoint PPT Presentation

Introduction to Computational Modeling of Social Systems

• Prof. Lars-Erik Cederman

Center for Comparative and International Studies (CIS) Seilergraben 49, Room G.2, lcederman@ethz.ch Nils Weidmann, CIS Room E.3, weidmann@icr.gess.ethz.ch http://www.icr.ethz.ch/teaching/compmodels Lecture, December 14, 2004

RePast Tutorial II

2

Today’s agenda

• IPD: Experimental dimensions
• EvolIPD model
• Random numbers
• How to build a model (2)
• Scheduling
• Homework C

3

Three crucial questions:

• 1. Variation: What are the actors’

characteristics?

• 2. Interaction: Who interacts with whom,

when and where?

• 3. Selection: Which agents or strategies are

retained, and which are destroyed?

(see Axelrod and Cohen. 1999. Harnessing Complexity)

4

Experimental dimensions

• 2 strategy spaces: B, C
• 6 interaction processes: RWR, 2DK, FRN,

FRNE, 2DS, Tag

• 3 adaptive processes: Imit, BMGA, 1FGA

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“Soup-like” topology: RWR

ALLC ALLC TFT ALLD ATFT TFT ALLD

In each time period, a player interacts with four other random players.

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2D-Grid Topology: 2DK

TFT ALLD ALLD ALLD TFT TFT ALLC ATFT ALLC

The players are arranged on a fixed torus and interact with four neighbors in the von-Neumann neighborhood.

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Fixed Random Network: FRN

ALLC ALLC TFT ALLD ATFT TFT ALLD TFT ATFT

The players have four random neighbors in a fixed random

• network. The relations

do not have to be symmetric.

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Adaptation through imitation

ALLC ALLC TFT ALLD ATFT TFT? ALLD

Neighbors at t Imitation

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Adaptation with BMGA

Comparison error (prob. 0.1)

2.8 6.0 0.8 9.0

Genetic adaptation

2.2

Fixed spatial neighborhood

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BMGA continued

Copy error (prob. 0.04 per “bit”)

2.8 6.0 0.8 9.0

Genetic adaptation

6.0

p=0; q=0 => p=1; q=0 Fixed spatial neighborhood

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Tutorial Sequence

December 7 SimpleIPD: strategy space Today EvolIPD: RWR December 21 GraphIPD: charts and GUI GridIPD: 2DK January 11 ExperIPD: batch runs and parameter sweeps

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EvolIPD: flowchart

setup() buildModel() resetPlayers() interactions() adaptation() reportResults() step()

play() play() remember() remember() addPayoff() addPayoff()

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Markovian vs. asynchronous adaptation

Markovian

t t-1

asynchronous

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Going sequential

private void stepMarkovian() { // We carry out four sub-activities: // Reset the agents' statistics // Loop through the entire agent list for (int i = 0; i < numPlayers; i++) { // Pick the agent final Player aPlayer = (Player) agentList.get(i); resetPlayer(aPlayer); } // Let them interact with their neighbors for (int i = 0; i < numPlayers; i++) { final Player aPlayer = (Player) agentList.get(i); interactions(aPlayer); } // FIRST STAGE OF DOUBLE BUFFERING! // Let all agents calculate their adapted type first for (int i = 0; i < numPlayers; i++) { final Player aPlayer = (Player) agentList.get(i); adaptation(aPlayer); } // SECOND STAGE OF DOUBLE BUFFERING! // Second, once they know their new strategy, // let them update to the new type for (int i = 0; i < numPlayers; i++) { final Player aPlayer = (Player) agentList.get(i); updating(aPlayer); } reportResults(); // Report some statistics } private void stepAsynchronous() { // We carry out four sub-activities: for (int i = 0; i < numPlayers; i++) { // Pick an agent at random final Player aPlayer = (Player) agentList.get( this.getNextIntFromTo(0, numPlayers - 1)); // Reset the agent's statistics resetPlayer(aPlayer); // Let it interact with its neighbors interactions(aPlayer); // Let it adapt adaptation(aPlayer); // Let it update its new type updating(aPlayer); } reportResults(); // Report some statistics }

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How to work with random numbers

• RePast full-fledged random number generator:

uchicago.src.sim.util.Random

• Encapsulates the Colt library random number

distributions: http://hoschek.home.cern.ch/hoschek/colt/

• Each distribution uses the same random number

stream, to ease the repeatability of a simulation

• Every distribution uses the MersenneTwister

pseudo-random number generator

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Pseudo-random numbers

• Computers normally cannot generate real

random numbers

• “Random number generators should not be

chosen at random” - Knuth (1986)

• A simple example (Cliff RNG):

X0 = 0.1 Xn+1 = |100 ln(Xn) mod 1|

x1 = 0.25850929940455103 x2 = 0.28236111950289455 x3 = 0.4568461655760814 x4 = 0.3408562751932891 x5 = 0.6294370918024157 x6 = 0.29293640856857195 x7 = 0.7799729122847907 x8 = 0.849608774153694 x9 = 0.29793011540822434 x10 = 0.08963320319223556 x11 = 0.2029456303939412 ...

20 40 60 80 100 120 140 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency

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“True” random numbers

• New service offered by the University of

Geneva and the company id Quantique http://www.randomnumber.info/

• No (yet) integrated into RePast

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Simple random numbers distribution

• Initialization:

Random.setSeed(seed); Random.createUniform(); Random.createNormal(0.0, 1.0);

• Usage:

int i = Random.uniform.nextIntFromTo(0, 10); double v1 = Random.normal.nextDouble(); double v2 = Random.normal.nextDouble(0.5, 0.3);

mean standard deviation standard deviation mean standard deviation Automatically executed by SimpleModel

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Available distributions

• Normal (or Gaussian)
• Pareto
• Poisson
• Uniform
• …
• Beta
• Binomial
• Chi-square
• Empirical (user-

defined probability distribution function)

• Gamma
• Hyperbolic
• Logarithmic

Beta Normal

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Custom random number generation

• May be required if two independent random number streams are

desirable

• Bypass RePast’s Random and use the Colt library directly:

import cern.jet.random.*; import cern.jet.random.engine.MersenneTwister; public class TwoStreamsModel extends SimModel { Normal normal; Uniform uniform; public void buildModel() { super.buildModel(); MersenneTwister generator1 = new MersenneTwister(123); MersenneTwister generator2 = new MersenneTwister(321); uniform = new Uniform(generator1); normal = new Normal(0.0, 1.0, generator2); } public void step() { int i = uniform.nextIntFromTo(0, 10); double value = normal.nextDouble(); } }

seeds

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How to build a model (2)

• If more flexibility is desired, one can extend

SimModelImpl instead of SimpleModel

• Differences to SimpleModel

– No buildModel(), step(), ... methods – No agentList, schedule, params, ... fields – Most importantly: no default scheduling

• Required methods:

public void setup() public String[] getInitParam() public void begin() public Schedule getSchedule() public String getName()

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SimModelImpl

import uchicago.src.sim.engine.Schedule; import uchicago.src.sim.engine.SimInit; import uchicago.src.sim.engine.SimModelImpl; public class MyModelImpl extends SimModelImpl { public static final int TFT = 1; public static final int ALLD = 3; private int a1Strategy = TFT; private int a2Strategy = ALLD; private Schedule schedule; private ArrayList agentList; public void setup() { a1Strategy = TFT; a2Strategy = ALLD; schedule = new Schedule(); agentList = new ArrayList(); } public String[] getInitParam() { return new String[]{"A1Strategy"}; }

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SimModelImpl (cont.)

public String getName() { return "Example Model"; } public void begin() { Agent a1 = new Agent(a1Strategy); Agent a2 = new Agent(a2Strategy); agentList.add(a1); agentList.add(a2); schedule.scheduleActionBeginning(1, this, "step"); } public void step() { for (Iterator iterator = agentList.iterator(); iterator.hasNext();) { Agent agent = (Agent) iterator.next(); agent.play(); } }

introspection

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SimModelImpl (cont.)

public String[] getInitParam() { return new String[]{"A1Strategy"}; } public int getA1Strategy() { return a1Strategy; } public void setA1Strategy(int strategy) { this.a1Strategy = strategy; } public static void main(String[] args) { SimInit init = new SimInit(); SimModelImpl model = new MyModelImpl(); init.loadModel(model, null, false); }

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How to use a schedule

• Schedule object is responsible for all the

state changes within a Repast simulation

schedule.scheduleActionBeginning(1, new DoIt()); schedule.scheduleActionBeginning(1, new DoSomething()); schedule.scheduleActionAtInterval(3, new ReDo()); tick 1: DoIt, DoSomething tick 2: DoSomething, DoIt tick 3: ReDo, DoSomething, DoIt tick 4: DoSomething, DoIt tick 5: DoIt, DoSomething tick 6: DoSomething, ReDo, DoIt

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Different types of actions

• Inner class

class MyAction extends BasicAction { public void execute() { doSomething(); } } schedule.scheduleActionAt(100, new MyAction());

• Anonymous inner class

schedule.scheduleActionAt(100, new BasicAction(){ public void execute() { doSomething(); } );

• Introspection

schedule.scheduleActionAt(100, this, "doSomething");

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Schedule in SimpleModel

public void buildSchedule() { if (autoStep) schedule.scheduleActionBeginning(startAt, this,"runAutoStep"); else schedule.scheduleActionBeginning(startAt, this, "run"); schedule.scheduleActionAtEnd(this, "atEnd"); schedule.scheduleActionAtPause(this, "atPause"); schedule.scheduleActionAt(stoppingTime, this, "stop", Schedule.LAST); } public void runAutoStep() { public void run() { preStep(); preStep(); autoStep(); step(); postStep(); postStep(); } } private void autoStep() { if (shuffle) SimUtilities.shuffle(agentList); int size = agentList.size(); for (int i = 0; i < size; i++) { Stepable agent = (Stepable)agentList.get(i); agent.step(); } }

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Scheduling actions on lists

• An action can be scheduled to be executed on

every element of a list:

public class Agent { public void step() { } } schedule.scheduleActionBeginning(1, agentList, "step");

• is equivalent to:

public void step() { for(Iterator it = agentList.iterator(); it.hasNext();) { Agent agent = (Agent) it.next(); agent.step(); } } schedule.scheduleActionBeginning(1, model, "step");

step() in SimpleModel step() in Agent

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Different types of scheduling

• scheduleActionAt(double at, …)

executes at the specified clock tick

• scheduleActionBeginning(double begin, …)

executes starting at the specified clock tick and every tick thereafter

• scheduleActionAtInterval(double in, …)

executes at the specified interval

• scheduleActionAtEnd(…)

executes the end of the simulation run

• scheduleActionAtPause(…)

executes when a pause in the simulation occurs

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Homework C

Modify the EvolIPD program by introducing a selection mechanism that eliminates inefficient players. The current adaptation() method should thus be modified such that the user can switch between the old adaptation routine, which relies

• n strategic learning, and the new “Darwinian” selection
• mechanism. The selection mechanism should remove the 10%

least successful players from the agentList after each round of

• interaction. To keep the population size constant, the same

number of players should be “born” with strategies drawn randomly from the 90% remaining players. Note that because it generates a population-level process, the actual selection mechanism belongs inside the Model class rather than in Player. Does this change make any difference in terms of the output?