Andrea

Why do we use simulation to study something?

Simulations are a method of “learning by doing” without actually “doing”. They allow researchers to imitate a process using a computer model, to observe how a system changes over time. According to Klaus Troitzsch, they are “…a thought experiment which is carried out with the help of a machine, but without direct interface to the target system.”

The use of a simulation to study something is optimal in many circumstances. Taking a look at examples in health care research, computer simulation can help with both explanatory and predictive tasks. A simulation may be useful for each of the following scenarios:

  • To study a complex system that cannot be adequately modeled using traditional methods. Computer simulation allows researchers to study complex systems without over-simplifying them to fit a mathematical model. For example, a population’s risk for malaria can be a complex combination of factors. Rather than simplifying the risk factors to fit a mathematical model, a computer simulation can be designed that accounts for all of the known factors. Such a simulation could be used to help researchers better explain why people contract the disease, or to predict the impact of proposed interventions.
  • To substitute for an experiment that cannot be done for pragmatic, theoretical, or ethical reasons. Sometimes data is too expensive to collect, or the time scale for data collection is too large. Observing how certain hereditary traits pass from one generation to the next (over more than two generations) might be an impossible task in “real life” but could be simulated using a computer model. Ethical issues also might arise in the collection of data to study a phenomenon. For example, studying the potential spread of a bioterrorism pathogen would be better done using a computer simulation than by actually exposing a population to the virus.
  • As a heuristic tool to develop hypothesis, models, and theories. A simulation can be helpful to learn more about a complex process prior to developing applicable hypotheses or theories. Simulating how malaria spreads through a population allows a public health researcher to “observe” the process first-hand before forming a hypothesis about how an intervention might help stop the disease. In the organizational side of healthcare research, a computer simulation might help a hospital develop a more efficient staffing model for their intensive care unit without using costly “trial and error”.
  • As a teaching tool, to gain understanding of a process. Particularly in the healthcare setting, simulations can be used as a training tool. For example, disaster response simulations whether on the computer or in “real life” can help the emergency department in a community hospital be prepared for an influx of patients due to a natural disaster or an outbreak of disease.

Even if analytical models are available for a given scenario, computer simulations may still add to our understanding of the system. There are benefits to be gained from redundancy and “cross-mapping” in research; simulations may provide new insights for traditional analytical models and vice versa.

When and why would you do simulations instead of, or in addition to, mathematical analysis like neo-classical economics?

Computer simulation can be complementary or preferred to mathematical analysis for research done in a wide range of fields, from economics to the social sciences. The note above (“Why do we use simulations to study something?”) outlines several examples of where simulations can be useful within a healthcare setting. In social science research, simulations can help to explain what is happening in the lab. The title of a paper written by Nan et al. says it all, “Beyond Being in the Lab: Using Multi-Agent Modeling to Isolate Competing Hypotheses” (Nan et al. 2005). The authors used computer simulation to help understand the results of their lab experiments about virtual teams, something they could not have easily done with mathematical analysis.

Particularly in economics, the common assumption for succinct mathematical models is rational human behavior. Given the nature of human beings, that can be a strong assumption to make. The idea of “bounded rationality” from game theory introduces scenarios in which humans might not act rationally. For example, they might lack sufficient information to make a rational decision, especially when more than one agent is involved, or the problem might be too complex for their mind to handle so they simplify it prior to making a decision. Mathematical analysis cannot always capture the complexity inherent in bounded rationality. Computer simulation, on the other hand, can mimic the inductive reasoning that human beings employ in such situations, and can therefore shed light not only on the problem but also on hypothetical explanations.

In the early 1990s, W. Brian Arthur used simulation to model an adaptive complex system problem inspired by the El Farol bar in Santa Fe (Arthur 1994). While later economists argued that this problem could be analyzed mathematically using the minority game (Zambrano 2004), Arthur used a simulation to define the problem and hypothesize explanations. This is an example of how the use of simulations can introduce and define a problem, to which mathematical analysis can help offer a partial explanation. But in order to fully understand the complexity of this problem, given that we do not know which decision model the agent will choose at any given point in time, a computer simulation is preferred. What we learn from this problem can be applied beyond the local pub; it sheds light on congestion problems in other areas like computer networks and automobile traffic.

Mathematical analysis can be complementary to computer simulations through the use of both Agent Based Modeling (ABM) and Equation Based Modeling (EBM). ABM looks at the behavior of each individual agent in a model, and might define each agent’s behavior using a differential equation. EBM looks uses differential equations to help define the larger picture, rather than each agent. These types of simulation have been used in the business context for Dynamic Analysis of Supply Chains (DASCh) (Van et al. 1998).

Bibliography
1. Arthur, W.B. "Complexity in Economic Theory: Inductive Reasoning and Bounded Rationality," The American Economic Review (84:2) 1994, p 6.
2. Nan, N., Johnston, W., Olson, J., and Bos, N. "Beyond Being in the Lab: Using Multi-Agent Modeling to Isolate Competing Hypotheses," in: Conference on Human Factors in Computing Systems, Portland, Oregon, 2005.
2. Van, H., Parunak, D., Savit, R., and Riolo, R. "Parunak, Savit, and Riolo, “Agent-Based Modeling vs. Equation-Based Modeling” Agent-Based Modeling vs. Equation-Based Modeling: A Case Study and Users ’ Guide," Modeling Agent Based Systems, Paris, 1998.
2. Zambrano, E. "The Interplay Between Analytics and Computation in the Study of Congestion Externalities: The Case of the El Farol Problem," Journal of Public Economic Theory (6:2) 2004, p 21.

Game of Life

My favorite examples of the Game of Life simulation:

1) Spiral Decay

2) Spark to Pi Fuse

3) Hexagonal Parity Flip

Turtle Models to share

1) Traffic Jams

2) Turtle Ecology

3) Forest Fire

The Evolution of Cooperation - Chapter 8

Consequences of additional forms of social structure – four factors:

Labels

  • definition: fixed characteristic of an agent (gender, skin color), observable by other players. Can lead to:
    • self-confirming stereotypes
    • disadvantage for minorities
    • status hierarchies

Reputation

  • definition: beliefs of other agents about how an agent will act (based on that agent’s prior interactions)
  • best reputation = bully

Regulation

  • definition: relationship between a government and the governed
  • roles of government:
    • set and enforce rules so that it pays for most of the governed to obey most of the time
    • settle disputes between private parties

Territoriality

  • definition: players interact with their neighbors rather than just anyone
  • Features
  • Proposition 8: If a rule is collectively stable, it is territorially stable
  • Effects
  • The way players interact with each other can affect the evolutionary process

Spatial Games

Spatial Games Reading Questions

Interesting Research

Interesting Research Essay

Additional Resources

Additional Resources

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License