1. This is easy to generalise to “dependent” products
Discrete Choice Model
This is easy to generalise to “dependent” products
“If a customer can buy one product from either Tesco, Amazon or Argos, then what is the probability that they choose Tesco?”
Set up a “Discrete Choice” model.
Parameterise model.
Solve all of Tesco’s (stated) problems.

2. Discrete Choice Model As a function of price… Market share of Tesco
Market share of Amazon

3. Discrete Choice Model Vectors of parameters Vector of prices
With N vendors, the market share for vendor i is:
Vectors of parameters
Vector of prices
Alternatively, we can use utility functions based on logistic distributions in a “standard” Discrete Choice Model framework

4. Discrete Choice Model Q1. How do we estimate the parameters?
Q2. How do we use parameterised model to maximise profit?

5. Discrete Choice Model Q1. How do we estimate the parameters?
Maximum Likelihood
Sketch idea:

6. Discrete Choice Model
Q2. How do we use parameterised model to maximise profit?
Equilibrium: each vendor is self-optimising
Expected profit of vendor i per unit product sold in whole market

7. Discrete Choice Model
This system can be solved analytically (or numerically)

8. Discrete Choice Model One quick concrete example to finish:
Three vendors (“red”, “blue” and “green”) all have unit cost £50. Suppose c1 = c2 = c3 = 1/3, but α1 = 1, α2 = 2 and α3 = 3. The prices are initially set to p1 = 100, p2 = 120 and p3 = 150. What happens if all vendors optimise profit?

9. Discrete Choice Model
Expected unit profit (£)
Price (£)

10. Discrete Choice Model
One quick concrete example to finish:
Three vendors (“red”, “blue” and “green”) all have unit cost £50. Suppose c1 = c2 = c3 = 1/3, but α1 = 1, α2 = 2 and α3 = 3. The prices are initially set to p1 = 100, p2 = 120 and p3 = 150. What happens if all vendors optimise profit?
SOLUTION: Prices will converge to the Nash equilibrium defined by p1 = 181.7, p2 = and p3 =
The Discrete Choice Model gives rise to a simple method of retrospective evaluation

11. Test Price Optimisation
Forecasting
Objective Function
Optimisation
Evaluation