Simulation Models as a Research Method

1. Simulation Models as a Research Method Professor Alexander Settles

2. Research Methodology - Simulation Simulation as a research tool Research in simulation Focus here is on simulation of discrete event dynamic systems

3. 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

4. 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

5. 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.

6. 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”

7. 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?

8. 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

9. 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

10. System Dynamics Research Tools • Add causal loops • Change mean of flow rates • Change variance of flow rates

11. System Dynamics Research Questions • How do organizations undergo fundamental change? • When do small interruptions create major catastrophes? • What conditions create system instability?

12. 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

13. NK Fitness landscape • (S, V, f) : • S: set of admissible solutions, • V : S → 2S function, :neighborhood • S → IR: fitness function.

14. 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

15. NK fitness landscapes • Vary N and K • Change adaptation moves • Add a “map” of the landscape • Create an environmental jolt

16. 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?

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

18. 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

19. Theoretical Logic • Optimization • Adaptation of a population of agents using an evolutionary process toward an optimal agent form

20. 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?

21. Genetic algorithms

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

23. 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

24. Research Questions • How does the pattern emerge and change? • How fast does a pattern emerge? • How do competition and legitimation affect density dependence?

25. 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

26. 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

27. Research Questions • What is the relationship between exploration and exploitation? • What is the optimal degree of structure?