An important assumption of the basic Bertrand Competition Model (MS-171 Bertrand Competition) is that all the Products in the Market are Commodities. Competitors drive Price down to Marginal Cost because Customers are ultimately indifferent to which Product they buy.

But this basic Bertrand Model is rarely seen in practice. Even Commodities have some form of Product Differentiation. The different terms and conditions of the sales contract may differentiate Commodities for business Customers even when nothing else does.

In this Market Simulation, we take the same workflow from MS-171 Bertrand Competition and introduce Product Differentiation. Like the other variations of the Bertrand Competition Model, the new model predicts that the Competitors will no longer drive Prices down to Marginal Cost and Profitability down to zero.

This Case Study provides a high-level overview of the workflow without detailed explanation. It assumes you are already somewhat familiar with KNIME and Market Simulation. If not, start by reviewing the Building Blocks and Community Nodes.

Adding Product Differentiation to the Market Simulation is, again, relatively easy. This time, a ‘Matrix Distributions‘ node is used to replace the ‘Product Generator‘ node.

The previous Product Generator node took a single input Customer Distribution for the Commodity and created two identical Willingness To Pay (WTP) Distributions for the two Products in the Market.

The new Matrix Distributions node creates two Customer Distributions that also have the same Mean Willingness To Pay (WTP), but this time they are not 100% perfectly correlated. In this case, the Correlation between the WTP Distributions for the two Products is 0.50.

When the Mean and Standard Deviation (SD) of two WTP Customer Distributions are the same, but the Correlation between the WTP Distributions is not 100% perfectly correlated, then the Products are said to be Horizontally Differentiated. See the ‘Differentiation Horizontal‘ node.

The Correlation between each individual Customer’s WTP can be observed by looking at the Output WTP Matrix (bottom port of the Matrix Distributions node). Customers who highly value Spacely Sprockets are also likely to highly value Cogswell Cogs, but now not to the same degree.

Configure Matrix Distributions

The Price Strategy trends for both Competitors can be compared and plotted after the usual 30 iterations of the Pricing Loop.

Like the earlier variations to the Bertrand Model (MS-172 Bertrand–Edgeworth Competition and MS-173 Bertrand Competition with Search Costs), Competitors in this Market no longer drive Price down to the Marginal Cost of $50, and Profit no longer trends towards zero. When Horizontal Differentiation (with Correlation = 0.50) is introduced, the Price of both Products stabilizes at about $93.00, with Profitability stabilizing at about $165,000.

But unlike the earlier Bertrand Variations, the Prices set by the two Competitors no longer follow a chaotic pattern. Product Differentiation leads to a pure Nash Equilibrium with steady-state Prices and Profitability.

Note the bumps in the output charts. This indicates that the expected Quantity and Profitability of both Products quickly become the actual Quantity and Profitability.

Chart #3
Profit