Posts Tagged ‘market dynamics’

What are “Mental Models”?

March 12th, 2010 14 comments

Editor’s note: This is part one of a two part series on Systems Thinking and mental models

In writing and teaching people about Systems Thinking, we often refer to “mental models”.  For some people, this comes as a bit of a surprise, because the context usually involves building models with the iThink or STELLA software.  They don’t expect us to start talking metaphysically about thinking.  “Is this about philosophy or modeling software?” they may wonder.  The software is actually a tool to help construct, simulate and communicate mental models.

Let’s define the term model: A model is an abstraction or simplification of a system.  Models can assume many different forms – from a model volcano in a high school science fair to a sophisticated astrophysical model simulated using a supercomputer.  Models are simplified representations of a part of reality that we want to learn more about.  George Box stated: “Essentially, all models are wrong, but some are useful”.  They are wrong because they are simplifications and they can be useful because we can learn from them.

So, what is a “mental model”?  A mental model is a model that is constructed and simulated within a conscious mind.  To be “conscious” is to be aware of the world around you and yourself in relation to the world.  Let’s take a moment to think about how this process works operationally.

Thinking about trees

Imagine that you are standing outside, looking at a tree.  What happens?  The lenses in your eyes focus light photons onto the retinas.  The photosensitive cells in your retinas respond by sending neural impulses to your brain.  Your brain processes these signals and forms an image of the tree inside your mind.

So at this point, we’ve only addressed the mechanisms by which you perceive the tree.  We have not addressed understanding what a tree is or considered changes over time.   We are dealing with visual information only.  There is nothing within this information that tells you what a tree actually is.

What makes the image of a tree in your minds click as an actual tree that exists right there in front of you?  This is where mental models kick in and you start to think about the tree.  The tree is actually a concept of something that exists in physical reality.  The “tree concept” is a model.  Understanding the concept of a tree requires more information than is available through sensory experience alone.  It’s built on past experiences and knowledge.

A tree is a plant.  It is a living thing that grows and changes appearance over time, often with the seasons.  Trees have root systems.  Trees use leaves for photosynthesis.  Wood comes from trees.  I can state these facts confidently because I have memories and knowledge of trees contained within my mental models.  Mental models contain knowledge and help us create new knowledge.


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Modeling Bass Diffusion with Rivalry

February 18th, 2010 4 comments

This is the last of a three-part series on the Limits to Growth Archetype.  The first part can be accessed here and the second part here.

Last time, we explored the effects of Type 1 rivalry (rivalry between different companies in a developing market) on the Bass diffusion model by replicating the model structure.  This part will generalize this structure and add Type 2 rivalry (customers switching between brands).

Bass Diffusion with Type 1 Rivalry

To model the general case of an emerging market with multiple competitors, we can return to the original single company case and use arrays to add additional companies.  In this case, everything except Potential Customers needs to be arrayed, as shown below (and available by clicking here).


For this example, three companies will be competing for the pool of Potential Customers.  Each array has one-dimension, named Company, and that dimension has three elements, named A, B, and C, one for each company.  Although each different parameter, wom multiplier, fraction gained per $K, and marketing spend in $K, can be separately specified for each company, all three companies use the same values initially.  All three companies, however, do not enter the market at the same time.  Company A enters the market at the start of the simulation, company B enters six months later, and company C enters six months after that.

Recall that the marketing spend is the trigger for a company to start gaining customers.  Thus, the staggered market entrance can be modeled with the following equation for marketing spend in $K:


The STEP function is used to start the marketing spend for each company at the desired time.  The ARRAYIDX function returns the integer index of the array element, so it will be 1 for company A, 2 for company B, and 3 for company C.  Thus, the offsets from the start of the simulation for the launch of each company’s marketing campaign are 0, 6, and 12, respectively.

This leads to the following behavior:


Note that under these circumstances, the first company to enter the market retains a leadership position.  However, companies B and C could anticipate this and market more strongly.  What if company B spent 50% more and company C spent 100% more than company A on marketing that is similarly effective?  This could be modeling by once again changing the equation for marketing spend in $K, this time to:

STEP(10 + (ARRAYIDX() – 1)*5, STARTTIME + (ARRAYIDX() – 1)*6)

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Developing a Market Using the Bass Diffusion Model

January 21st, 2010 2 comments

This is part two of a three part series on Limits to Growth.  Part one can be accessed here and part three can be accessed here.

In part one of this series, I explained the Limits to Growth archetype and gave examples in epidemiology and ecology. This part introduces the Bass diffusion model, an effective way to implement the capture of customers in a developing market. This is also used to implement what Kim Warren calls Type 1 rivalry in his book Strategy Management Dynamics, that is, rivalry between multiple companies in an emerging market.

The Bass Diffusion Model

The Bass diffusion model is very similar to the SIR model shown in part one. Since we do not usually track customers who have “recovered” from using our product, the model only has two stocks, corresponding loosely to the Susceptible and Infected stocks. New customers are acquired through contact with existing customers, just as an infection spreads, but in this context this is called word of mouth (wom). This is, however, not sufficient to spread the news of a good product, so the Bass diffusion model also includes a constant rate of customer acquisition through advertising. This is shown below (and can be downloaded by clicking here).


The feedback loops B1 and R are the same as the balancing and reinforcing loops between Susceptible and Infected in the SIR model. Instead of an infection rate, there is a wom multiplier which is the product of the Bass diffusion model’s contact rate and the adoption rate. If you are examining policies related to these variables, it would be important to separate them out in the model.

The additional feedback loop, B2, starts the ball rolling and helps a steady stream of customers come in the door. If you examine the SIR model closely, you will see that the initial value of Infected is one. If no one is infected, the disease cannot spread. Likewise, if no one is a customer, there is no one to tell others how great the product is so they want to become customers also. By advertising, awareness of the product is created in the market and some people will become customers without having encountered other customers who are happy with the product.

The behavior of this model is shown below. Note it is not different in character from the SIR model or the simple population model.

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Modeling Customers Switching Between Brands – The General Case

October 23rd, 2009 5 comments

This is the last installment of a four-part series.  The first three parts can be accessed by clicking on the links below.
Methods for Using Arrays Effectively

Modeling a Watershed with Arrays
Modeling Customers Switching Between Brands

Generalizing the Model

When I showed Steve Peterson (at Lexidyne) my brand switching model, he told me there is a more general version that separates the customer loss fraction from the fraction won by another competitor.  This has been presented in Pharmaceutical Product Strategy by Mark Paich, Corey Peck, and Jason Valant.

In my original formulation, the switching probability matrix was the product of these two variables.  However, in many practical cases, the data available comes from two different places and reflects these two separate components.  The revised model structure is shown below.


Instead of one composite switching probability, this model uses a switching out probability that is distinct from the switching in probability.  The switching out probability is a one-dimensional array that, for each product, contains the fraction of customers lost to rivals every time unit (in our case, month).  A sample for the five brands A, B, C, D, and E appears below.

Brand Fraction Lost
A 0.091
B 0.170
C 0.046
D 0.026
E 0.071

switching out probability

We can see from this table that Brand B is losing 17% of its customers to rivals each and every month!  Whoever is managing that product had better do something quickly.

The other side of the story has to do with which brand the customers are switching to.  The switching in probability matrix contains, for each brand, the fraction of lost customers that migrate to a rival brand.  Thus, each row of this matrix must add up to one (100% of lost customers).  A sample appears below.

From\To A B C D E
A 0.00 0.11 0.33 0.55 0.01
B 0.18 0.00 0.29 0.41 0.12
C 0.22 0.02 0.00 0.44 0.32
D 0.04 0.00 0.77 0.00 0.19
E 0.02 0.07 0.28 0.63 0.00

switching in probability

Note the diagonal will always be zero.

We can determine a lot of things from this table.  For example, brand B offers no competition to brand D, brand D is the biggest rival of all the other brands, and brand C is brand D’s biggest rival.

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Modeling Customers Switching Between Brands

September 30th, 2009 1 comment

This is the third installment of a four-part series.  The other three parts can be accessed by clicking on the links below.
Methods for Using Arrays Effectively

Modeling a Watershed with Arrays
Modeling Customers Switching Between Brands – The General Case


In the second post of this series, I showed how to selectively pull information from an array in order to route water through a watershed.  In this post, I will use the exact same technique to move customers between different product brands.

Switching Customers between Different Products

Business models often need to model gaining customers from, and losing customers to, competing products in a relatively mature market (what Kim Warren, in his excellent book Strategy Management Dynamics, calls “Type 2 Rivalry”).  These are often driven with statistical models developed through market research.  For this application, we need a matrix describing the probability of switching from product A to product B each time unit.  A sample appears in the table below.

From\To A B C D E
A 0.000 0.010 0.030 0.050 0.001
B 0.030 0.000 0.050 0.070 0.020
C 0.010 0.001 0.000 0.020 0.015
D 0.001 0.000 0.020 0.000 0.005
E 0.001 0.005 0.020 0.045 0.000

switching probability (units: dimensionless)

To read this table, locate the product the customer is presently using in the left column (say, B).  Read across that row (the second row, in this case) until you find the product the customer is switching to (say, C).  The number in that cell (in this case, 0.05 or 5%) is the probability the customer will switch from the first product to the second (from B to C) in this time unit.  If the model is running in months, as ours is, this table indicates that 5% of customers using product B switch to product C every month.

Of course, the values in the table do not need to be constant.  Often each cell will contain a regression equation based on various product characteristics – including market share, marketing effort, product features, and product quality – that evolve over the course of the simulation.

Note the diagonal is zero.  This means customers do not switch from one product to the same product.

Note also that the sum in any row cannot exceed 1.0, which represents 100% of the customers using that product.  It is quite normal for it to be below 1.0 because we do not include people who are not switching.  Some modelers find it easier to always have each row add up to 1.0.  If you desire to do this, fill the diagonal with the difference between 1.0 and the sum of the other columns.  For example, to do this for product A, replace the top left cell with 1.0 – (0.01 + 0.03 + 0.05 + 0.001) = 0.909 [for you Beatles fans].


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