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Discrete Choice Model

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.

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Discrete Choice Model

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  1. 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 Market share of Tesco As a function of price… Market share of Amazon

  3. Discrete Choice Model 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 = 2and α3= 3. The prices are initially set to p1 = 100, p2 = 120and 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 = 2and α3= 3. The prices are initially set to p1 = 100, p2 = 120and p3= 150. What happens if all vendors optimise profit? SOLUTION: Prices will converge to the Nash equilibrium defined by p1 = 181.7, p2 = 124.9and p3= 108.2. The Discrete Choice Model gives rise to a simple method of retrospective evaluation

  11. Test Price Optimisation Forecasting Objective Function Optimisation Evaluation

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