Search Costs

Variation of Bertrand Competition

The basic Bertrand Competition Model was explored in the workflow: MS-171 Bertrand Competition. In that model, all firms set their own price, with each firm assuming the other competitors in the market will not change price. Joseph Bertrand predicted that Competitors of Commodity Products will always reduce Price down to an unprofitable Marginal Cost.

The basic Bertrand Competition Model required all Customers to have perfect knowledge of all Products and Prices in the Market. But in reality, many Customers do not wish to overcome the Search Costs involved and hence are only aware of some of the Product choices available to them.

In this Market Simulation, we take the same workflow from MS-171 Bertrand Competition and modify it to account for these Search Costs. 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.

Add Search Costs

Adding Search Costs to the Market Simulation is relatively easy with a ‘Demand Shredder‘ node.

The Demand Shredder node starts with an upstream Customer Willingness To Pay (WTP) Matrix. For each Customer row (C00001 to C10000), the node eliminates Product options from the Customer’s awareness by setting the Customer’s WTP for those Products to zero.

In this case, the Demand Shredder node has been configured to always preserve the Customer’s first choice. But then the node is set so that there is only a 20% chance the Customer is aware of the Competitive alternative.

The ‘GroupBy’ node aggregates the number of choices each Customer has. Of the 10,000 total Customers in the Market, it shows:

  • 40% of Customers are only aware of the Spacely Sprockets Product (about 4,000 Customers)
  • 40% of Customers are only aware of the Cogswell Cogs Product
  • 20% of Customers are aware of both (although these Customers are split on which is their first choice).

Configure Demand Shredder

WTP Matrix with Shredded Demand

Group-By Node

Group-By Counts

New Price Trend

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

Like the earlier alternative MS-172 Bertrand–Edgeworth Competition that considered Capacity Constraints, the Price in this Market Simulation no longer trends towards Marginal Cost of $50, and Profit no longer trends towards zero. When Search Costs are introduced, the Price of both Products hovers between $64 and $70, with Profitability hovering between $60,000 and $80,000.

And like the Edgeworth Paradox, the Prices set by the two Competitors follow a chaotic pattern. A pure Nash Equilibrium with steady-state Prices is never reached.

Pricing Loop Results

Chart #1
Price vs Cost

Chart #2
Expected Quantity

Chart #3