Identifying members who are likely to move to a lower cost alternative product Overview:
I am looking for some technical direction from the ML/data science community about how I could tackle my business problem. 

Context:
In a nutshell, I have a group of customers who repeatedly purchase products from a category of products e.g. the frying pan category. In the frying pan category there are 15-20 different manufacturers of frying pans. Each of the different frying pans have different features i.e. large, small, non-stick, stainless steel, dishwasher proof etc. but essentially they're all frying pans. Some people buy the premium product while others buy the budget and some others buy the mid range product.

The most popular brand of product is the most expensive and is a loss making product for us. There is however another product (mid range product) that has nearly the exact same characteristics as the expensive pan but is half the cost and generates the most profit for my company.     

Objective:
I would like to identify those customers who currently purchase the most expensive product and reach out to them based on their likelihood of purchasing the mid range product to convince them of the benefits of the mid range pan. 

Approaches:
I thought one approach to this would be to find the members who buy the expensive product but are most similar in characteristics/features of the mid range purchasers and offer them a discount to incentivize them to switch products. To achieve this I would use a user - user similarity measurement rather than an item - item similarity measure. 

The data:
I have access to a swathe of demographic information, purchase history data, product detail characteristics so building analytical base tables is not a problem. 

If you have any suggestions as to how I could approach this problem I would be very grateful for your insights.
We could analyze the customer's purchase history. Here, for the sake of explanation let's assume that customers A and B. First, we'll make the purchase history of customer A,


We'll calculate the frequency of customer A buying the mid-range pan. Also, we'll need the total number of purchases made by the customer. So, for customer A you'll get a ratio which is ( number of purchases of the mid-range pan ) / total purchases.
Similarly, we'll calculate such ratios for the expensive pans both for customers A and B.
Next, we'll compare the ratios for all customers and select the highest N customers who most probably will buy the mid-range or expensive pan.


Why are using the ratios ( or precisely, the probabilities of buying a certain pan )?


We'll need customers who are frequent buyers of a particular pan. These are more chances of switching a product rather than the less frequent customers.
As they are regular customers, they will be more influenced by the discount available on the mid-range pan.



  You may use various metrics to aggregate the customers who can have a product transition. You may also have a look at Bayes Theorem which I think will be appropriate too. It will give the answer- "Which are customers which have the highest probability of buying a mid-range pan given that they have already bought a expensive pan.