Market Optimization

Bertrand Competition

This Market Simulation illustrates the result of a Price War between two identical (commodity) Products. The Bertrand Competition model predicts that when commodity Products engage in a Price War, Price would be reduced to Marginal Cost and Profitability would be zero.

From Wikipedia [Bertrand Competition]:

Bertrand argued that if firms chose prices [rather than quantities using a Cournot model], then the competitive outcome would occur with price equal to marginal cost. The model rests on very specific assumptions. There are at least two firms producing a homogeneous (undifferentiated) product and cannot cooperate in any way. Firms compete by setting prices simultaneously and consumers want to buy everything from a firm with a lower price (since the product is homogeneous and there are no consumer search costs). If two firms charge the same price, consumers demand is split evenly between them. It is simplest to concentrate on the case of duopoly where there are just two firms, although the results hold for any number of firms greater than 1.

See also: Wikipedia [Perfect Competition]

In this Market Simulation, two Competitive Rivals are selling the exact same ‘Sprockets’ Product. The Products are commodities and completely undifferentiated. The Competitors initially sell at the same (Profitable) Price, but they soon start a Price War. The Price War takes place over a number of (internal) iterations in which each Competitor privately evaluates the results from three experiments:

  1. raise Price,
  2. lower Price, or
  3. keep the existing Price.

The top-half of this Market Simulation workflow explores what would happen if each Competitor engaged in only a single round of discounting.

The bottom-half of the workflow explores the outcome from an unrestrained Price War.

Because the Scientific Strategy premium Price War nodes can run the Price experiments internally (without an external loop) the calculations can be completed much more quickly than the Free Community Edition nodes.

See also the similar Market Simulation that uses only Free Community Edition nodes: BB-113 Commodity Competitive Loop

This Case Study provides provides a glimpse into the premium Market Optimization nodes. These premium nodes are not available in the Free Community Edition of Scientific Strategy. But a selection of problems that can be solved with the Free Community Edition nodes can be found in Case Studies and Market Simulation.

#1 Benchmark Market

The ‘Product Generator’ node generates a Market comprising of two identical Products:

  • RivalA.Sprockets
  • RivalB.Sprockets

The ‘Simulate Market’ node then initializes the Market by predicting how many Customers would select each Product.

See also:

Product Array

WTP Matrix


#2 Single Discount

If each Competitor were restricted to a single round of discounting then their Prices would decrease but their Profitability would improve.

This workflow branch shows how the Price War node first calculates an expected result for each single Competitor as if their Price adjustment was the only change in the Market. The Price War node then calculates an actual result when all the Price changes from all the Competitors are simultaneously taken into account.

Input Product Array

Input WTP Matrix

Price War #1

Price War #1

Output #1
Price War

Notes: The top part of the Price War Output shows the expected Market conditions assuming only RivalA changed Price. RivalA’s Quantity would increase from 777 units to 4,568 units. The second part shows the expected Market conditions assuming only Rival B changed Price. The last part shows the combined result when all Competitors change Price. These results show that, while RivalA and RivalB will not get their expected result, they will increase the Quantity they each sell to over 2,000 units.


Notes: The final output shows three result rows for RivalA:

  • Before (initial Market)
  • Expected Results
  • After (final Market)

#3 Price War

The bottom-half of this Market Simulation workflow shows the results of a unrestrained Price War between RivalA and RivalB over 50 rounds. While Prices decline and Quantities increase, the Profitability of both Competitors heads to zero.

Product Array

WTP Matrix

Price War #2

Chart #1

Chart #2

Chart #3