Agent-Based Modeling and Simulation (ABMS) Bertan Badur Department of Management Information Systems Boğaziçi University

The Business Investor Model Chapter 10, 11, 12 of Agent-Based and Individual- Based Modeling: A Practical Introduction, by S. F. Railsback and V. Grimm NetLogo User Menual

Outline 10.4 Putting Sensing to Work: The Business Investor Model

The Business Investor Model What information agents have and how they get it Model: –How people decide what business to invest in. Businesses differ –annual profit –risk of failure – the investor loses its all wealth Pathces – business alternatives Turtles – investors –sence neigbor businesses

The ODD Description No cost of entering or switching

Entities, State Variables, and States Entities: –investor agents (tutrtles) –businesses (patches) with profits and risk State variables: –inverstors – location, wealth (money units) –businesses – annual profit (P) (money per year) probability of failure (F) per year – loses all wealth Lanscape - 19x19 no wrapping Time scale – ticks every year, 25 years

Process Wverwiew and Scheduling in each time step actions executed in the orders: Investor repositioning: –look at their neighbnoring businesses –if they have better profit risk trade off –move to that business –only one agent at a patch –in random order Accounting: –update wealth: previous + current profit – if business fails wealth becomes zero Output: –The world display plots and an output file is updated

ODD – Design Concepts Basic principles emergence adaptive behavior objetive U = (W + Th*P)(1 - F) Th –W current welth –Th time horizon –P profit of patch –F faling rate of patch prediction sensing interraaction stochasticity observation

globals [n-inv th mean-w std-w one-up-std one- down-std count-f] turtles-own [w] patches-own [p f]

to setup ca set n-inv 150 set th 5 crt n-inv [ move-to one-of patches with [not any? turtles- here] ] ask patches [ set p (random-float 9000) set f (random-float 0.09) ] reset-ticks end

to go tick set count-f 0 ask turtles [ inv-repos acc-w ] set mean-w mean [w] of turtles set std-w standard-deviation [w] of turtles set one-up-std mean-w + std-w set one-down-std mean-w - std-w ; plot mean-w ; plot one-down-std ; plot one-up-std output-print (word ticks" " mean-w " "count-f) if ticks = 25 [stop] end

to go tick ask turtles [ inv-repos acc-w ] if ticks = 25 [stop] end

inv-repos and utility-for to inv-repos let po-patchs (patch-set patch-here neighbors with [not any? turtles- here]) if any? po-patches [ let best-patch max-one-of po-patchs [utility-for myself] move-to best-patch ] end to-report utility-for [t] let cw [w] of t let u (cw + th * p ) * (1 - f) ^ th report u end

acc-w to acc-w ifelse random-float 1.0 < f [ set w 0 set count-f count-f + 1 ] [set w w + p] end

observationoutput add to the go procedure add globlas and initilize in setup set mean-w mean [w] of turtles set std-w standard-deviation [w] of turtles set one-up-std mean-w + std-w set one-down-std mean-w - std-w ;in the intrface ; plot mean-w ; plot one-down-std ; plot one-up-std output-print (word ticks" " mean-w " "count-f)

sensing radius add a variable sensing radius –s-r with a slider to inv-repos let po-patchs (patch-set patch-here patches in- radius s-r with [not any? turtles-here]) let best-patch max-one-of po-patchs [utility-for myself] move-to best-patch end

Networks set n-of-links 5 crt n-inv [ move-to one-of patches with [not any? turtles- here] create-links-to n-of n-of-links other turtles ]

modify positioning to inv-repos let po-patchs (patch-set patch-here neighbors with [not any? turtles-here]) set po-patchs (patch-set (po-patchs) ( [neighbors with [not any? turtles-here]] of out-link-neighbors)) let best-patch max-one-of po-patchs [utility-for myself] move-to best-patch end

Chpater 11: Adaptive Bevavior and Objectives

1. Introduction and Objectives Most important reason - ABM: How system behavior is effected from adaptive bahvior of its individual agents –how agents make decisions –change their states effected from environments and themselfs Adaptation –decision to changes in environment Objectives

agent behavior – something an agent does systems behavior – dynamics of the system of agents traits – rules given to agents about how to behave adaptive behavior – decision made to improve their states with respect to an objective –implicit or explicit adaptive trait - rules for adaptive behaior theory – adaptive traits to be tested

Objectives The objective adaptive behavior –fitness – ecology – organizms -increase probablity of offsprings –utility – economics objective function –explicit measure of agents fitness or utility Set of alternatives – evaluted by objective function trade-offs –one objective increasing the other decreasing more profit – more risk increase proift avoid risk more food – more chance of eaten by others

Learning Objectives Subseting agentsets in NetLogo design and analysis of experiments for adaptive trifts modeling trade-off decision. –maximizing an objective function and satisficing

Identifying and Optimizing Alternatives in NetLogo adaptive traits. –identifying alternatives –eliminating infeasible alternatives –evaluating feasible alternatives – objective function –selecting best alternative – maximizing objective In NetLogo – alternatives as agents –patches – turtles to move to –turtles for interacting –links to follow

Identifying Decision Alternatives by Subseting NotLogo Agentsegts Start with agentsets turtles decision move to a patch the agentset – patches – set of all alternatives neighbors – moving to neighboring pathces other alternatives: –turtles, links – all turtles or links –turtles-here, turtles-at, turtles-on – turtles on specific pathces –link-neighbors, in-link-neighbors- out-link-neighbors – tutles at other end of the calling turtle’s links

other –all but the agent executing the statement in-radius, in-cone –agents with in a specified distance or distance and angle let destination-pathces patches in-radius 3 Creating a new agentset – –not new agents but –references to existing agents with-max, max-n-of, with-min: –evaluate a reporter chose the agnets maximizing the value of teh reporters let furtune-50 max-n-of 50 turtles [net-worth]

with let potential-mates other turtles with [age > 20] set potential-mates potential-mates with [sex != [sex] of mayself ] set potential-mates potential-mates with [ not maried? ] or let potential-mates other turtles with [age > 20 and sex != [sex] of mayself and not maried? ]

Optimize and Objective Function max-one-of, min-one-of –reprots an agent –in case of a tie select one randomlay with-max, with-min –all agents as an agentset Do the NetLogo Brainteasers

Adaptive Behavior in the Business Inverstor Model Experiments in BehaviorSpace new variables –profit-multiplier - from 0.5 to 1.0 –risk-multiplier – from 1.0 to replications Plots –mean final invertor weath v.s. profit mutiples of baseline –mean anual profit v.s. profit mulitples of baseline see figure 11.1 –mean final invertor weath v.s. risk mutiples of baseline –mean anual profit v.s. risk mulitples of baseline see figure 11.2

Non Optimizing Adaptive Traits: A Satisficing Example In practice – not optimization satisficing – finding alternatives good enough Not observe profits or risks of Decision –change more frequently – objective not met well –change less frequently – compare objective fuction with atreshold value

investors can only observe current projects profit and risk values compare expected anula change in expected welth with a treshold value –riskles rate of investments - 5& w-i-tr in globlas set its vaue in setup or add a slider

reposition turtles to inv-repos if w-i-r < w-i-tr [ let po-patchs neighbors with [not any? turtles-here] if any? po-patchs [ move-to one-of po-patchs ] ] end

reoprt rate of change of welth to-report w-i-r ; reports rate of change of expected welth if w = 0 [ set w 1 ] let u (w + th * p ) * (1 - f) ^ th let wir (u - w) / (w * th) report wir end

The Objective Function In the Business Invertor model some projects have negative profit –profit drawn from a uniform dist to10000 If investor’s weath fall below 0 –set it to zero if expected value at the end of time horizon is negative –set it to zero count failing projects due to –negative profit –random failure

Other Objective Functions First –in the baseline model Second –ignore risk – based on only profit Third –ignore profit –only risk of failure or negagtive profits

Chapter 12: Prediction

1. Introduction and Objectives Fondomental to many decisions –anticipate consequences of alternatives prediction – by itself a model modeling how the agent models Holland (1995) – tacit prediction –hidden assupmptions explicit prediction –Business Invertor model – calculates expected value of projects What predictions are esential? How to model them Modelingpredictions How different predictions affect outcomes of AMBs

Learning Objectivesw effect of diferent predictions on outcomes submodel analysis counter plots Bayesian updating

2 Effect of Prediction: BusinessInvesgtor Model Time Horizon What is the effect of time horizon on invertors welth;? BehaviorSpace –mean anual profit v.s. time horizon –meqn final wealth v.s. time horizon

3 Implementing and Analysing Submodels submodels – processes designing, testing nad analizing seperately Analyze expected utility utility function of profit and failure rate coutour plots of expected welth v.s. profit and risk

4. Analizing the Investor Untilityh Function profit and risk changes how expected welth varies parameters time horizon and current welth Take total derivatie of utility with respect to profit and risk equate to zero

5. Modeling Prediction Explicitly Estimating risk of patches from historical data –from overall failure rates – mean rate of failure –from historcal data of the patch <Bayesian statistics priaory of a binomial parameter – beta distribution Guessing overall failure rate Start with mean variance of overall failure rate –mean : 0.5 –varince ( ) 2 /