ock market fluctuations, commodity prices, etc) over the short term. In addition, using chaos theory, pricing decision-makers have been able to estimate how long the projections may be useful.

Over the longer term, while the paths of individual chaotic trajectories cannot be predicted accurately for very long, knowledge of the system attractors provides useful information about the long-term trends in system/industry behavior. In chaos theory, the 'strange attractor' plays an organizing role, as the order or pattern at the heart of what appears to be chaos. For example, if you’re packing to go to Minneapolis in January, you’ll pack very differently than if you were going to Miami, without any current weather information. So, in Minneapolis the basic attractor is such that the temperatures trend to a point that will be below freezing. You would have made your packing decisions based on some knowledge of the system trends. One major producer of surfactants in Europe, knowing that market dynamics were such that an industry attractor was leading to rapid price declines, used that knowledge to offer 10% discounts upfront for the signing of one-year contracts. At the end of the year, other competitors were facing 50% lower prices.

CONTROLLING CHAOS
Chaos theory helps first, by recognizing that an attractor can help understand and manipulate the industry or system since the attractor gives form and structure to behavior that we might otherwise dismiss as random. Second, if you can find an attractor for an industry (system), then any disturbances to the current state will still render its partic

How many times have you and your company, debated and fought over the potential outcomes of a particular pricing strategy, only to have seemingly random, unpredictable factors rear their ugly heads? How many analytical tools have you used: game theory, forecasting, market research, decision-tree analyses,… only to realize that none of these was able to help predict much beyond the next quarter or less. Welcome to our wonderful world of chaos!

So what is happening? Just as in the movie, Jurassic Park, industries evolve in a very dynamic way given complex interactions. As in nature, very small disturbances can lead to significantly different outcomes- a reflection of a chaotic system.

Briefly, chaos theory considers nonlinear systems. In a linear system, if I do A then I know that B will happen and C will happen as a result of this. But, according to chaos theory, a number of variables will change what happens between A and B and then between B and C. Again, as in Jurassic Park, a butterfly may flap its wings and its rains in Central Park. There are a few points to be aware of when thinking about the impact of chaos on pricing: There are deterministic relationships between the participants in a chaotic system but only patterned outcomes and not predictable, outcomes result. In the business world, outcomes reflect very complex underlying relationships that include the interaction of several potentially chaotic systems; crop prices for example, are influenced by the interaction of economic and weather systems. While, chaos theory provides guidance on crop price cycle patterns, it says that it’s basically impossible to predict exactly the size of the fluctuations or their timing.

Chaos theory, however, does say that prices will vary between particular boundaries. In chaotic systems, small disturbances multiply over time because of nonlinear relationships and the dynamic, repetitive nature of chaotic systems. As a result, such systems are extremely sensitive to initial conditions. For example, Dell’s mail order strategy forced other companies to reduce their prices and reexamine their traditional high-cost sales and service channels.

While you might think that by obtaining better models and a more accurate specification of starting conditions, better forecasts would result. Chaos theory suggests that the payoff from developing more accurate models may be small. Oil companies recognize this and have developed pricing models that take into account the numerous factors that could influence prices at the pump- making ongoing adjustments to prices. In contrast to game theoretic models that predict equilibrium outcomes, chaotic systems do not reach a stable equilibrium. They never pass through the same state more than once. The implication is that industries do not settle down and any apparent stability for example, in pricing, is likely to be short-lived.

A chaotic system constantly changes based on the feedback that results from the actions of players in the system

Chaotic behavior can take place on an attractor, in which case, a large set of initial conditions will lead to convergence towards a particular pattern of behavior.

USING CHAOS THEORY IN PRICING STRATEGY
Use Of Feedback
The results of chaos theory help us know what transitions to expect when we add feedback to a system and suggest ways to adjust feedback.

For example, suppose that you observe a change in your competitor’s behavior based on how often you change your prices. Normally, your competitor may not change prices when you make no price changes; but, if you have adjusted your prices, the competitor responds by changing prices on some key products. Should you double your rate of price changes to twice a year, your competitor may then change prices on all products. You have cut the time difference between significant events in half and observe a transition in the system. While it is not clear exactly how you can predict the next transition in competitive behavior by decreasing the time between price changes, you should at least be alert that the next transition in this system could occur only if we increase the frequency of price changes by a small amount. Such an understanding of the chaotic dynamics should help you understand and control your own response, selected from a flexible range of options, given the likely transitions tested when the system control parameters were tested.

Another key use of feedback being introduced into a system so as to create chaos is the relative timing of an incursion on a competitive decision cycle (it may even be more important than the magnitude of the incursion). Many successful strategies hinge on “getting inside the decision cycle” of the competitor. The idea is to take some pricing action and then move with such agility as to make a subsequent move before the competitor has time to orient, observe, decide and act (OODA, to use a military term) in response to your first pricing move. Chaos theory offers an important new insight into this basic strategy: we should expect ranges of different responses depending on how tightly we approach the duration of the OODA loop. That is, to outpace the competitor that may operate on a semi-annual basis, revising prices on a quarterly basis may produce the same disruption and disorientation as would revisions on a monthly or weekly basis. You could then focus planning on other factors such as brand investment, efficient use of resources and so on. The idea is that you should expect ranges of control parameter values where the system behavior is relatively consistent; but you should also note parameter ranges where small adjustments produce drastic changes in response. If you were an IC manufacturer with facilities to improve efficiencies more quickly than your competitors, you may want to introduce small but frequent, price changes to disrupt the market and drive competitors out that cannot follow the efficiencies and maintain margins.

PREDICTABILITY
HOW DOES chaos theory explain, reduce or increase predictability?

In the near-term chaos can be used to uncover patterns and sub patterns that are not apparent and this information can be used to project the behavior of an industry that has irregular dynamics. Chaos analysts have been able to tease out competitors pricing activities by using techniques that allow them to find information embedded within a mass of background noise ( the economy, stock market fluctuations, commodity prices, etc) over the short term. In addition, using chaos theory, pricing decision-makers have been able to estimate how long the projections may be useful.

Over the longer term, while the paths of individual chaotic trajectories cannot be predicted accurately for very long, knowledge of the system attractors provides useful information about the long-term trends in system/industry behavior. In chaos theory, the 'strange attractor' plays an organizing role, as the order or pattern at the heart of what appears to be chaos. For example, if you’re packing to go to Minneapolis in January, you’ll pack very differently than if you were going to Miami, without any current weather information. So, in Minneapolis the basic attractor is such that the temperatures trend to a point that will be below freezing. You would have made your packing decisions based on some knowledge of the system trends. One major producer of surfactants in Europe, knowing that market dynamics were such that an industry attractor was leading to rapid price declines, used that knowledge to offer 10% discounts upfront for the signing of one-year contracts. At the end of the year, other competitors were facing 50% lower prices.

CONTROLLING CHAOS
Chaos theory helps first, by recognizing that an attractor can help understand and manipulate the industry or system since the attractor gives form and structure to behavior that we might otherwise dismiss as random. Second, if you can find an attractor for an industry (system), then any disturbances to the current state will still render its particu

basically impossible to predict exactly the size of the fluctuations or their timing.

Chaos theory, however, does say that prices will vary between particular boundaries. In chaotic systems, small disturbances multiply over time because of nonlinear relationships and the dynamic, repetitive nature of chaotic systems. As a result, such systems are extremely sensitive to initial conditions. For example, Dell’s mail order strategy forced other companies to reduce their prices and reexamine their traditional high-cost sales and service channels.

While you might think that by obtaining better models and a more accurate specification of starting conditions, better forecasts would result. Chaos theory suggests that the payoff from developing more accurate models may be small. Oil companies recognize this and have developed pricing models that take into account the numerous factors that could influence prices at the pump- making ongoing adjustments to prices. In contrast to game theoretic models that predict equilibrium outcomes, chaotic systems do not reach a stable equilibrium. They never pass through the same state more than once. The implication is that industries do not settle down and any apparent stability for example, in pricing, is likely to be short-lived.

A chaotic system constantly changes based on the feedback that results from the actions of players in the system

Chaotic behavior can take place on an attractor, in which case, a large set of initial conditions will lead to convergence towards a particular pattern of behavior.

USING CHAOS THEORY IN PRICING STRATEGY
Use Of Feedback
The results of chaos theory help us know what transitions to expect when we add feedback to a system and suggest ways to adjust feedback.

For example, suppose that you observe a change in your competitor’s behavior based on how often you change your prices. Normally, your competitor may not change prices when you make no price changes; but, if you have adjusted your prices, the competitor responds by changing prices on some key products. Should you double your rate of price changes to twice a year, your competitor may then change prices on all products. You have cut the time difference between significant events in half and observe a transition in the system. While it is not clear exactly how you can predict the next transition in competitive behavior by decreasing the time between price changes, you should at least be alert that the next transition in this system could occur only if we increase the frequency of price changes by a small amount. Such an understanding of the chaotic dynamics should help you understand and control your own response, selected from a flexible range of options, given the likely transitions tested when the system control parameters were tested.

Another key use of feedback being introduced into a system so as to create chaos is the relative timing of an incursion on a competitive decision cycle (it may even be more important than the magnitude of the incursion). Many successful strategies hinge on “getting inside the decision cycle” of the competitor. The idea is to take some pricing action and then move with such agility as to make a subsequent move before the competitor has time to orient, observe, decide and act (OODA, to use a military term) in response to your first pricing move. Chaos theory offers an important new insight into this basic strategy: we should expect ranges of different responses depending on how tightly we approach the duration of the OODA loop. That is, to outpace the competitor that may operate on a semi-annual basis, revising prices on a quarterly basis may produce the same disruption and disorientation as would revisions on a monthly or weekly basis. You could then focus planning on other factors such as brand investment, efficient use of resources and so on. The idea is that you should expect ranges of control parameter values where the system behavior is relatively consistent; but you should also note parameter ranges where small adjustments produce drastic changes in response. If you were an IC manufacturer with facilities to improve efficiencies more quickly than your competitors, you may want to introduce small but frequent, price changes to disrupt the market and drive competitors out that cannot follow the efficiencies and maintain margins.

PREDICTABILITY
HOW DOES chaos theory explain, reduce or increase predictability?

In the near-term chaos can be used to uncover patterns and sub patterns that are not apparent and this information can be used to project the behavior of an industry that has irregular dynamics. Chaos analysts have been able to tease out competitors pricing activities by using techniques that allow them to find information embedded within a mass of background noise ( the economy, stock market fluctuations, commodity prices, etc) over the short term. In addition, using chaos theory, pricing decision-makers have been able to estimate how long the projections may be useful.

Over the longer term, while the paths of individual chaotic trajectories cannot be predicted accurately for very long, knowledge of the system attractors provides useful information about the long-term trends in system/industry behavior. In chaos theory, the 'strange attractor' plays an organizing role, as the order or pattern at the heart of what appears to be chaos. For example, if you’re packing to go to Minneapolis in January, you’ll pack very differently than if you were going to Miami, without any current weather information. So, in Minneapolis the basic attractor is such that the temperatures trend to a point that will be below freezing. You would have made your packing decisions based on some knowledge of the system trends. One major producer of surfactants in Europe, knowing that market dynamics were such that an industry attractor was leading to rapid price declines, used that knowledge to offer 10% discounts upfront for the signing of one-year contracts. At the end of the year, other competitors were facing 50% lower prices.

CONTROLLING CHAOS
Chaos theory helps first, by recognizing that an attractor can help understand and manipulate the industry or system since the attractor gives form and structure to behavior that we might otherwise dismiss as random. Second, if you can find an attractor for an industry (system), then any disturbances to the current state will still render its partic

Use Of Feedback
The results of chaos theory help us know what transitions to expect when we add feedback to a system and suggest ways to adjust feedback.

For example, suppose that you observe a change in your competitor’s behavior based on how often you change your prices. Normally, your competitor may not change prices when you make no price changes; but, if you have adjusted your prices, the competitor responds by changing prices on some key products. Should you double your rate of price changes to twice a year, your competitor may then change prices on all products. You have cut the time difference between significant events in half and observe a transition in the system. While it is not clear exactly how you can predict the next transition in competitive behavior by decreasing the time between price changes, you should at least be alert that the next transition in this system could occur only if we increase the frequency of price changes by a small amount. Such an understanding of the chaotic dynamics should help you understand and control your own response, selected from a flexible range of options, given the likely transitions tested when the system control parameters were tested.

Another key use of feedback being introduced into a system so as to create chaos is the relative timing of an incursion on a competitive decision cycle (it may even be more important than the magnitude of the incursion). Many successful strategies hinge on “getting inside the decision cycle” of the competitor. The idea is to take some pricing action and then move with such agility as to make a subsequent move before the competitor has time to orient, observe, decide and act (OODA, to use a military term) in response to your first pricing move. Chaos theory offers an important new insight into this basic strategy: we should expect ranges of different responses depending on how tightly we approach the duration of the OODA loop. That is, to outpace the competitor that may operate on a semi-annual basis, revising prices on a quarterly basis may produce the same disruption and disorientation as would revisions on a monthly or weekly basis. You could then focus planning on other factors such as brand investment, efficient use of resources and so on. The idea is that you should expect ranges of control parameter values where the system behavior is relatively consistent; but you should also note parameter ranges where small adjustments produce drastic changes in response. If you were an IC manufacturer with facilities to improve efficiencies more quickly than your competitors, you may want to introduce small but frequent, price changes to disrupt the market and drive competitors out that cannot follow the efficiencies and maintain margins.

PREDICTABILITY
HOW DOES chaos theory explain, reduce or increase predictability?

In the near-term chaos can be used to uncover patterns and sub patterns that are not apparent and this information can be used to project the behavior of an industry that has irregular dynamics. Chaos analysts have been able to tease out competitors pricing activities by using techniques that allow them to find information embedded within a mass of background noise ( the economy, stock market fluctuations, commodity prices, etc) over the short term. In addition, using chaos theory, pricing decision-makers have been able to estimate how long the projections may be useful.

Over the longer term, while the paths of individual chaotic trajectories cannot be predicted accurately for very long, knowledge of the system attractors provides useful information about the long-term trends in system/industry behavior. In chaos theory, the 'strange attractor' plays an organizing role, as the order or pattern at the heart of what appears to be chaos. For example, if you’re packing to go to Minneapolis in January, you’ll pack very differently than if you were going to Miami, without any current weather information. So, in Minneapolis the basic attractor is such that the temperatures trend to a point that will be below freezing. You would have made your packing decisions based on some knowledge of the system trends. One major producer of surfactants in Europe, knowing that market dynamics were such that an industry attractor was leading to rapid price declines, used that knowledge to offer 10% discounts upfront for the signing of one-year contracts. At the end of the year, other competitors were facing 50% lower prices.

CONTROLLING CHAOS
Chaos theory helps first, by recognizing that an attractor can help understand and manipulate the industry or system since the attractor gives form and structure to behavior that we might otherwise dismiss as random. Second, if you can find an attractor for an industry (system), then any disturbances to the current state will still render its partic

move before the competitor has time to orient, observe, decide and act (OODA, to use a military term) in response to your first pricing move. Chaos theory offers an important new insight into this basic strategy: we should expect ranges of different responses depending on how tightly we approach the duration of the OODA loop. That is, to outpace the competitor that may operate on a semi-annual basis, revising prices on a quarterly basis may produce the same disruption and disorientation as would revisions on a monthly or weekly basis. You could then focus planning on other factors such as brand investment, efficient use of resources and so on. The idea is that you should expect ranges of control parameter values where the system behavior is relatively consistent; but you should also note parameter ranges where small adjustments produce drastic changes in response. If you were an IC manufacturer with facilities to improve efficiencies more quickly than your competitors, you may want to introduce small but frequent, price changes to disrupt the market and drive competitors out that cannot follow the efficiencies and maintain margins.

PREDICTABILITY
HOW DOES chaos theory explain, reduce or increase predictability?

In the near-term chaos can be used to uncover patterns and sub patterns that are not apparent and this information can be used to project the behavior of an industry that has irregular dynamics. Chaos analysts have been able to tease out competitors pricing activities by using techniques that allow them to find information embedded within a mass of background noise ( the economy, stock market fluctuations, commodity prices, etc) over the short term. In addition, using chaos theory, pricing decision-makers have been able to estimate how long the projections may be useful.

Over the longer term, while the paths of individual chaotic trajectories cannot be predicted accurately for very long, knowledge of the system attractors provides useful information about the long-term trends in system/industry behavior. In chaos theory, the 'strange attractor' plays an organizing role, as the order or pattern at the heart of what appears to be chaos. For example, if you’re packing to go to Minneapolis in January, you’ll pack very differently than if you were going to Miami, without any current weather information. So, in Minneapolis the basic attractor is such that the temperatures trend to a point that will be below freezing. You would have made your packing decisions based on some knowledge of the system trends. One major producer of surfactants in Europe, knowing that market dynamics were such that an industry attractor was leading to rapid price declines, used that knowledge to offer 10% discounts upfront for the signing of one-year contracts. At the end of the year, other competitors were facing 50% lower prices.

CONTROLLING CHAOS
Chaos theory helps first, by recognizing that an attractor can help understand and manipulate the industry or system since the attractor gives form and structure to behavior that we might otherwise dismiss as random. Second, if you can find an attractor for an industry (system), then any disturbances to the current state will still render its partic

ock market fluctuations, commodity prices, etc) over the short term. In addition, using chaos theory, pricing decision-makers have been able to estimate how long the projections may be useful.

Over the longer term, while the paths of individual chaotic trajectories cannot be predicted accurately for very long, knowledge of the system attractors provides useful information about the long-term trends in system/industry behavior. In chaos theory, the 'strange attractor' plays an organizing role, as the order or pattern at the heart of what appears to be chaos. For example, if you’re packing to go to Minneapolis in January, you’ll pack very differently than if you were going to Miami, without any current weather information. So, in Minneapolis the basic attractor is such that the temperatures trend to a point that will be below freezing. You would have made your packing decisions based on some knowledge of the system trends. One major producer of surfactants in Europe, knowing that market dynamics were such that an industry attractor was leading to rapid price declines, used that knowledge to offer 10% discounts upfront for the signing of one-year contracts. At the end of the year, other competitors were facing 50% lower prices.

CONTROLLING CHAOS
Chaos theory helps first, by recognizing that an attractor can help understand and manipulate the industry or system since the attractor gives form and structure to behavior that we might otherwise dismiss as random. Second, if you can find an attractor for an industry (system), then any disturbances to the current state will still render its particular evolution unpredictable (think of a swinging tire). But any, transient behavior eventually dies out, and the global system behavior trends are unchanged. Third, there is some hope of predicting basins of attraction, so that in initiating pricing moves, you can set up initial conditions so that the systems evolves under its own dynamics towards the trends of the attractor that you want. For example, if you were the lowest cost producer in a price sensitive market with a large number of aggressive competitors, by taking a small decrease in price you would likely initiate a price war. The attractor, industry movement towards the lowest price, would ultimately favor you, as the lowest cost producer.

KEY LEARNINGS
By thinking about your industry as a chaotic system, you need to be aware of the extent to which uncertainties can disrupt the industry and dramatic change can occur unexpectedly- so flexibility and adaptiveness in pricing are necessary As a result, you need to identify the key metrics that will provide you with sufficiently fast feedback so that the chaos does not get to the extreme boundaries that chaotic systems can reach.

By testing and understanding the dynamics of a chaotic system, you can mitigate the potential downside of a chaotic industry.

Most importantly, Chaos can be controlled. Chaos theory demonstrates that a chaotic system, previously thought of as random, can be influenced so that it becomes stable. Small changes can make big differences. There are three techniques for doing this, described above.

Regular periodic disturbances can be introduced into the system so that the system responds in a manner that will see it evolve into the longer term trends that you may want based on an attractor describing the longer-term recurrent behavior that you want in an industry.

Real-time measurements of the system output to determine how far to adjust the selected control parameter ( think of keeping a yardstick balanced on the palm of your hand; by moving your hand a bit, you keep the yardstick balanced). While this requires a constant feedback loop, a stable output is reached intentionally, and not in a “hit and miss manner”.

Extensive calculations can be developed to approximate the dynamics of the system’s attractor.