Market Optimization

Orthogonal Competition

This Market Simulation illustrates the result of a Price War between two differentiated Products. Unlike Bertrand Competition, competing differentiated Products can both remain Profitable even after a Price War.

The term “orthogonal” describes a specific type of differentiation. According to Wikipedia:

… independent variables that affect a particular dependent variable are said to be orthogonal if they are uncorrelated.

In other words, one Product is said to be orthogonal to another if the Willingness To Pay (WTP) Customer Distribution of the first Product is uncorrelated with that of the second.

Examples of Orthogonal Products might include carnival attractions or theme park rides: your like (or dislike) of the “Ring Toss” game might be unrelated to how much you like the “Spin-A-Wheel” game or the “Disk Drop” game. Other examples might include international food, and movie categories (is your enjoyment of an action movie reflective of how much you like a drama?).

But see also the next Market Simulation MO-113 Semi-Orthogonal Price War for a discussion of Semi-Orthogonal Products and how Product Categories (for example, carnival-entertainment vs movie-entertainment) can impact the differentiation between Products.

In this Market Simulation, two Competitive Rivals are selling orthogonally differentiated Products in the Sprocket Market. These results are designed to be compared to the previous Market Simulation: MO-111 Commodity Price War

As before, the two Competitors initially sell at the same (Profitable) Price and soon start a Price War. However, in this case one of the Competitors suffers from a Cost disadvantage. This would have spelt certain doom under Bertrand Competition, but here both Competitors find that they can profitably survive.

As before, 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-131 Orthogonal 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 ‘Customer Distributions’ node generates a Market comprising of two differentiated Products, each having an uncorrelated Willingness To Pay (WTP) Matrix:

  • RivalA.Sprockets
  • RivalB.Sprockets

Note that RivalA has a Cost advantage of  $40 per Sprocket compared to a Cost of $50 per Sprocket for RivalB.

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

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. Unlike the previous MO-111 Commodity Price War Market Simulation, the gap between the expected result and the actual result is far smaller for Orthogonal Products.

Input Product Array

Input WTP Matrix

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 1540 units to 4,911 units.

The second part shows the expected Market conditions assuming only RivalB changed Price. RivalB does not expect to increase Quantity as much as RivalA because it’s Cost disadvantage drives up RivalB’s Profit Maximizing Price.

The last part shows the combined result when all Competitors change Price. These results show that, although RivalA and RivalB will not get their expected result, they will still significantly increase the Quantity they each sell (RivalA will still sell over 4,000 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.

Unlike the previous MO-111 Commodity Price War, the Prices in this Market Simulation quickly stop declining and level out. RivalB’s ultimate steady-state Price is higher than the RivalA Price because RivalB’s Cost disadvantage causes it to seek a different Profit Maximizing Price.

The Price War node illustrates that it is not to the advantage of either Competitor to seek any further Price discounts – even if the Competitor’s Rival were to maintain their old Price. A stable Price Equilibrium has therefore been reached.

Product Array

WTP Matrix

Price War #2

Chart #1

Chart #2

Chart #3