Business, Law, and Innovation

System Dynamics

Spring 2011

Professor Adam Dell

The University of Texas School of Law

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What is System Dynamics?

• System dynamics is the application of systems theory to the behavior of complex systems.

• To review, systems theory is:• “The basic idea of system theory is that all things in the

universe (rivers; baseball games; galaxies) can be viewed as discrete systems, operating under a defined set of rules. While the systems may be different, they exhibit strikingly similar behavior. If different systems behave similarly, perhaps it's because they are connected.”

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What are complex systems?

• There are various definitions, but for our purposes “complex systems” are systems in which there are multiple interactions between many different components (or agents).

• A complex system is characterized by multiple agents whose interactions give rise to structural effects that aren’t apparent in the agents themselves.

• For example, an ant colony is a complex system — its structure is highly dependent on the characteristics of individual agents, but you can’t derive the structure of an ant colony by studying individual ants.

• A car, on the other hand, is merely a machine — complicated, but its operation can be understood by studying the component parts.

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Basic Concepts: Stocks and Flows

• A Stock is a variable measured at a specific point in time.

• A Flow is the rate of change in a particular variable.

• (In calculus terms, a stock is an initial quantity plus the integral of a flow, and a flow is the derivative of a stock over time)

• For example:

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Stock

Flows

Births DeathsPopulationPopulation

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Basic Concepts: Feedback loops

• Positive / negative feedback loops, delayed loops

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PopulationPopulationBirths Deaths

Available Resources

Births have a positive feedback effect,but it’s delayed (think baby boomers)

Population increases take up available resources, which decreases the birth rate (a negative feedback effect)

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Examples of Models

• Any investment could be modeled by its costs and profits. The question is what happens in between.

• A bad model may describe some reality but still lack explanatory power or detail.

• A good model reflects reality while remaining flexible and providing explanatory power.

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A (too) simple model

• This model may reflect reality, but isn’t that useful:

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A complex but useful model

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Life Insurance in the UK:

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Complex adaptive systems

• Complex adaptive systems are a conceptual subset of complex systems that adapt to their environment

• Examples:• Agent: a single ant

• Complex (multi-agent): an ant farm

• Complex Adaptive: an ant colony

• Agent: an employee

• Complex (multi-agent): a firm

• Complex Adaptive: a market

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Don't Be Confused

• All of the previous examples could be characterized as “complex” or “adaptive” on some level (all life is “complex,” even ants) — but we use different levels of abstraction depending on the analysis:

• For example, we don't necessarily need to know the physiology of an ant to study its colony — it's enough that we can make generalizations about groups of ants.

• In fact, a “complex adaptive” system may be easier to analyze than its “complex” components; e.g., markets are less chaotic than firms.

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On the other hand...

• Of course, details do matter:(ant biology is important if the colony faces an epidemic)

• But we can’t know or model everything.

• Therefore, we have to consider:• What's difficult to discover versus simply unknowable (which

assumptions are unavoidable)

• Whether an incorrect assumption can be corrected later (which errors matter most)

• What information is valuable and why (cost-benefit of research)

• How much error the system can tolerate (volatility, constraints)

• “Fools ignore complexity. Pragmatists suffer it. Some can avoid it. Geniuses remove it.” — Alan Perlis

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Systems Thinking

• We also don't have to model every system in order to take advantage of system dynamics principles; just thinking in terms of systems can be helpful:

• First, systems thinking can be applied broadly: All systems tend to exhibit certain behaviors that we can learn to isolate and recognize, and that can give us a decided advantage even if we can't formally analyze every system.

• Second, systems are everywhere — not just business. Thinking in terms of systems gives us a means to approach problems in other disciplines, and a way to apply the lessons learned in one field to another.

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Systems Thinking

• Third, systems thinking focuses us on the things that matter — inputs and outputs, rival behavior, tolerances, repeated effects: high-level dynamics...

• Fourth, systems thinking is a very powerful abstraction:

• The inputs and outputs of a system can be easily changed to model different organizational goals or even different value networks

• Systems are modular, so the same organization can be modeled even if it contains very dissimilar systems

• This modularity is also flexible — it can help organize our thinking when dealing with very difficult problems, like merging two organizations or adapting to new market conditions

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System Behaviors

•“One can only display complex information in the mind. Like seeing, movement or flow or alteration of view is more important than the static picture, no matter how lovely.” — Alan Perlis

•By studying complex systems, we can learn to recognize certain consistent patterns produced in such systems, what causes those patterns, and the effects they produce.

•Here are some examples (some we’ve seen before):

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Feedback Effects: Entropy

• Entropy is the amount of randomness in a system• Decreasing entropy increases stability, but at the cost of

energy loss

• High entropy indicates free energy in a system that can be captured, but also significant instability

• Feedback effects tend to amplify entropy

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Feedback Effects: Equilibria

• Systems often settle into a stable state (equilibrium); the interesting question is how they can be knocked out of those states

• Systems can have multiple equilibria:• Tipping points and chasm-crossing can be thought of as

moving between equilibria

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Common Patterns: Golden Mean

• Certain formations tend to beubiquitous in complex systems:

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Common Patterns: Order or Chaos?

• [Wolfram]

• [Cellular automata: order disguised as chaos]

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Chaotic Effects

• [Complex systems exhibit chaotic effects; sensitivity to initial conditions]

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Chaotic Effects: Nonlinearity

• Chaotic systems exhibit nonlinear effects — i.e., linear changes cause qualitative changes in state

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Chaos

Complexity

Order

Linear Change

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Network Effects

• [Network effects are very important to systems! They have important impacts on system dynamics models because linear inflows lead to exponential outflows]

• [Network effects have another, subtle aspect -- if you interconnect two systems exhibiting network effects, or combine two stocks feeding network effects, the resulting change is exponential]

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Emergence

• A system can be more than the sum of its parts!

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Wisdom

• However, systems thinking and system dynamics are just tools. Someone has to make and maintain a model, and a model is only as good as its data. This skill (art?) requires discipline and practice.

• We must make consistently good assumptions; errors are bad, but systemic errors will be fatal.

• Therefore, in order to effectively analyze systems, we need reliable ways of adapting our models and avoiding systemic or repeated errors.

• We have to recognize bias, and we must be self-critical: this is part of what we mean by "wisdom."

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