Simulation Models as a Research Method

Professor Alexander Settles

Research Methodology - Simulation

• Simulation as a research tool

• Research in simulation

• Focus here is on simulation of discrete event dynamic systems

Social Simulation• Most social science research uses some kind of theory or model

– Theories are generally stated in textual form

– But some are represented as equations

– Sometimes carry out experiments on artificial social systems that would be impossible or unethical to perform on human populations

• One advantage: must think through your assumptions

– Clarity and precision; each parameter needs a value

– All the detail of the model can be inspected by others

• Disadvantage: data adequate for estimating all parameter values may be hard to get

Sociology and Complexity• The physical world is full of systems that are (almost) linear

• But (human) societies have quite unpredictable features

– Their characteristics at any one time are affected by their past histories (‘path dependence’)

– E.g., adoption of 1 of a pair of alternative technologies by a society can be greatly influenced by minor contingencies about who chooses which technology early on

• Human societies, institutions and organizations are complex systems

– The behavior of the system as a whole can’t be understood in terms of the separate behaviors of its parts

– Contrasts with reductionist physical sciences

Simulation as a Research Tool

• Why simulation?– An analytical approximation has been developed

to model some system performance measure.– The development of the approximation requires

simplifying assumptions/approximations.– The conjecture is that the analytical model is still a

reasonable representation of the real system.– Simulation is being used to support or refute this

conjecture.

Simulation as a Research Tool

• Are the assumptions applied in the simulation clearly stated?– Distributions used.– Operational protocols, e.g., blocking, etc.– Correlation? – Can you simulate the same system?

• Steady State vs. Terminating – Number of runs – Length of runs

• Some models take a long time to “settle down”

Simulation as a Research Tool

• Verification & validation– Mainly applies to studying a real system or a

detailed representation– How was this conducted?

• Results compared to an existing system?• Comparisons made to existing analytical results?• Extreme cases tested?

Simulation as a Research Tool

• Experimental design– Experimental design?– Random systems?

• The importance of this depends on the way the simulation was used– If simulating to understand a system and

gain insight, these issues become more important

Methods of simulation

• System dynamics– Behavior of a system with complex causality

and timing– System of intersecting, circular causal loops– Stocks that accumulate and dissipate over

time– Flows that specify rates within system– Inputs to a system of interconnected causal

loops, stocks, and flows produce system outcomes

System Dynamics Research Tools

• Add causal loops• Change mean of flow

rates• Change variance of

flow rates

System Dynamics Research Questions

• How do organizations undergo fundamental change?

• When do small interruptions create major catastrophes?

• What conditions create system instability?

NK fitness landscapes

• Speed and effectiveness of adaptation of modular systems with tight versus loose coupling to an optimal point

• System of N nodes, K coupling between nodes

• Fitness landscape that maps performance of all combinations

NK Fitness landscape

• (S, V, f) :• S: set of admissible

solutions,• V : S → 2S

function, :neighborhood

• S → IR: fitness function.

Key Assumptions

• Adaptation via incremental moves and long jumps

• Optimization

• Adaptation of a modular system using search strategies (i.e., long jumps, incremental moves) to find an optimal point on a fitness landscape

NK fitness landscapes

• Vary N and K

• Change adaptation moves

• Add a “map” of the landscape

• Create an environmental jolt

NK fitness landscapes

• How long does it take to find an optimal point (e.g., high-performing strategy)?

• What is the performance of the optimal point?

• What is the optimal strategic complexity?

• How does cognition improve experiential learning?

Genetic algorithms

• Adaptation of a population of agents (e.g., organizations) via simple learning to an optimal agent form

Genetic algorithms

• Adaptation of a population of agents (e.g., organizations) via simple learning to an optimal agent form

• Population of agents with genes• Evolutionary adaptation (v-s-r) • Variation via mutation (mistakes) and

crossover (recombination)• Selection via fitness (performance)• Retention via copying selected agents

Theoretical Logic

• Optimization

• Adaptation of a population of agents using an evolutionary process toward an optimal agent form

Research Questions

• How does adaptive learning occur within bargaining?

• How does organizational learning affect the evolution of a population of organizations?

• What affects the rate of adaptation (or learning or change)?

• When and/or does an optimal form emerge?

Genetic algorithms

Cellular automata

• Emergence of macro patterns from micro interactions via spatial processes (e.g., competition, diffusion) in a population of agents

Cellular automata

• Population of spatially arrayed and semi-intelligent agents

• Agents use rules (local and global) for interaction, some based on spatial processes

• Neighborhood of agents where local rules apply

Research Questions

• How does the pattern emerge and change?

• How fast does a pattern emerge?

• How do competition and legitimation affect density dependence?

Stochastic processes

• One or more processes by which system operates

• One or more stochastic sources (e.g., process elements)

• Probablistic distributions for each stochastic source

Definition

• A stochastic process is one whose behavior is non-deterministic in that a system's subsequent state is determined both by the process's predictable actions and by a random element.

• Manufacturing process

• Finance – asset pricing – Markov chain

Research Questions

• What is the relationship between exploration and exploitation?

• What is the optimal degree of structure?