Market Simulation

Leader-Follower

The Stackelberg Leadership Model is a strategic game in which the Market Leader moves first, then the Market Follower sets its ‘Best Response’.

The Market Leader can take advantage of this model as it can first predict the Follower’s Best Response, then set its own strategy accordingly. A Nash Equilibrium is reached because both the Market Leader and Market Follower set optimal strategies based upon the strategy of the other.

When the Stackelberg Leadership Model was first developed in 1934, the two firms in the model competed on Quantity. Hence the model was an alternative to Cournot Competition, with the Stackelberg Leadership Model resulting in lower Prices and greater total output Quantity.

But this Market Simulation is based upon Price Competition. Here, the Market Leader has a Cost Advantage over the Follower who sells a very similar (but not identical) Product.

The Leader is required to have perfect information, so can accurately predict the Follower’s Best Response. The Follower need not have perfect information, but is required to act rationally and not blackmail the Leader into adopting an alternative strategy.

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.

Downloads

KNIME Workflow
Workflow Image

Leader Calculations

Both the Leader and the Follower sell similar Products, and Customers have an average Willingness To Pay (WTP) of $100 for each. The Market is defined by Horizontal Differentiation, so individual Customers will perceive Product values differently, and the WTP Customer Distribution for the two Products will be uncorrelated.

But the Market Leader can manufacture its Products for $50, while the Market Follower can only manufacture its Products for $60. Hence the Market Leader has a $10 Cost Advantage which it can use to strategically punish the Market Follower if required.

To calculate the Follower’s Best Response to all scenarios, the Market Leader sweeps its own Price from $70 to $200 (in $5 increments) using the ‘Tuning Loop Start‘ node. The Leader then predicts how the Follower would react to each Test Price.

Cost Advantage

Price Sweep

Test Market

Follower: Best Responses

Once the Leader sets the Test Price (sweeping incrementally from $70 to $200) it is up to the Follower to set their Best Response. The ‘Price Maximize‘ node is configured to automatically calculate the Profit Maximizing Price of the Follower (given the Test Price of the Leader). The downstream nodes then convert the results into Flow Variables that can be tracked across each iteration of the Tuning Loop.

Price Maximize Node

Profit Maximizing Price

Track Iteration Results

Leader: Best Strategy

The Leader continues to calculate and gather the Follower’s Best Responses to all its Test Prices (from $70 to $200) using the Tuning Loop End Node. This Tuning Loop End Node is configured to catch the Test Price that maximizes the Leader’s Profitability (given the Follower’s Best Response).

A Nash Equilibrium is reached when the Price set by the Leader, and the Best Response by the Follower, are:

  • Leader Price = $100
  • Follower Price = $110

The bottom two ports of the Tuning Loop End Node are used to take a snapshot of the Market conditions (Product Array and WTP Matrix) at the point where the Leader’s Profitability is maximized. Pass-through MetaNodes are used to collect these Market conditions during each loop iteration.

The final downstream Line Chart nodes plot the Price / Market Share / Revenue / Profitability for both the Leader and Follower at every Test Price.

Loop End Node

Pass-Thru Meta-Node

Nash Equilibrium Prices

Follower Best Responses

Leader Maximized Profit