# Stackelberg Model

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21 Aug, 2024

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Table Of Contents

## What Is the Stackelberg Model?

*The Stackelberg model is a leadership model that allows the firm dominant to set its price first. Subsequently, the follower firms optimize their production and cost. It was formulated by Heinrich Von Stackelberg in 1934.*

It helps analyze competition between firms where the leader makes the decision while others follow. The leader has better access to technology, production methods, cost, and a larger market. In certain sectors, like telecom, automobiles, etc, there is always one dominant firm where this model is used.

##### Table of contents

- The Stackelberg model is a game theory model in economics that analyzes market competition between firms.
- After a time-lapse, the first two scenarios will result in an equilibrium condition where the profit maximization functions will serve as the determinants.
- In case 3, a warfare situation will occur as equilibrium will be challenging to establish. Therefore, such a loggerhead stance can only be eliminated if a collision or failure of the weaker firm leads to a monopoly in the market.
- Finally, in case 4, the profit maximization expectations will not hold, and they must revise.

### Stackelberg Model Explained

The **Stackelberg model of oligopoly** remains an essential strategic model in economics. This model is helpful to a firm when it realizes profitability prospects under the first-mover advantage concept. A practical instance where leaders commit to the first move is capacity expansion. It is assumed that one cannot undo the action.

In principle, Stackelberg's strategy is essential, where the first mover, the leader, acts irrespective of the follower's movement.

It makes decisions depending on the advantage that it has over its followers. The followers respond to it after considering the market conditions and their own cost and benefit.

The advantage that the leader gets is in the form of better technology and innovation, a larger customer base, lower cost of production, etc. There is a sequential decision-making process which the leader makes, and the followers follow.

The **Stackelberg model of oligopoly** is a useful tool in the oligopoly market and can be used to understand the market dynamics and make future predictions.

### Assumptions

The **Stackelberg model game theory **follows certain assumptions as mentioned in the list below:

- A duopolist can sufficiently recognize market competition based on the Cournot model.
- Each firm aims to maximize its profits based on the expectation that the decisions of its competitors will not be affected by its output.
- It assumes perfect information for all players in the market.
- Note: An underlying assumption with the Cournot model is that the operating firms cannot collude and must seek to maximize profits based on their rivals’ decisions.
- The Stackelberg model follows a sequential move pattern and is not simultaneous. We can say that the leader who naturally has the first-mover advantage takes control of the output and hence, price setting.
- Following the above argument, the Stackelberg leader firms have a smaller market share, and profit margins.

However, models such as Stackelberg, Cournot, and Bertrand have assumptions that do not always hold in real markets. While one firm may follow Stackelberg's principles, the other might not. Thus, be creating a situation of complexity.

### Calculations

The following steps can help solve a basic problem based on the **Stackelberg model game theory**:

**Write the demand function for the market.****Write the cost functions for both firms A and B in the market.****The individual reaction functions in the duopoly are found by taking the partial derivates of the profit function.****Assume firm A as a leader, and obtain the profit maximization equation for firm A, substituting firm B’s profit function in firm A equation.****Solve for firm B as being the follower.**

### Example

Let us assume a market with three players – A, B, and C. If A is the dominant force, it will set the product's price first. After that, firms B and C will follow the price set and adjust their production basis supply and demand patterns accordingly. Thus, we see that the firm A has a **stackelberg model first mover advantage.**

### Possible Scenarios

The following circumstances are possible if two firms, A and B, participate in a duopolistic competition:

- Firm A chooses to be the leader, and B wants to be the follower.
- Firm B chooses to be the leader, and A wants to be the follower.
- Both A and B want to be the leaders.
- Both A and B choose to be followers.

### Graph

An important genesis of this model is that one of the Stackelberg leaders produces more output than it would have made under the Cournot equilibrium. Similarly, the follower in the Stackelberg model stimulates less production than that in the Cournot model. To demonstrate **stackelberg model first mover advantage**, look at the graphical representation below: -

Assuming the X-axis represents firm A's production and Y-axis for firm B's output. Then, the quantities Qc and Qs indicate an equilibrium point for Cournot and Stackelberg conditions, respectively.

If firm A assumes itself as the Stackelberg leader and B as the follower, it will produce Qa’ quantity. Consequently, firm B follows with Qb’, which is the best it can maximize up to. Notice that Qs is the Stackelberg equilibrium point where firm A produces more than it could create at Qc, the Courton equilibrium point.

Similarly, when firm B follows after firm A has taken the output decision, it produces much less than it could have in a Courton game.

### Stackelberg Vs Other Models

The comparison of the Stackelberg model to the other models is given below:

Parameters | Stackelberg | Cournot | Bertrand |
---|---|---|---|

Quantity | Medium | Low | High |

Price | Medium | High | Low |

Type of Move | Sequential | Simultaneous | Simultaneous |

**The similarity to the Cournot Model**** **

- Both models assume quantity to be the basis of competition.
- Both models assume homogeneity of products instead of the Bertrand model, including theory on differentiated products.

### Frequently Asked Questions ( FAQs)

**What is the Stackelberg model of oligopoly?**

The made Stackelberg model of oligopoly is on the non-cooperative strategic game. First, a firm (leader) determines how much to create in this model. Then, all the other firms (followers) conclude how much to produce later.

**What is the Stackelberg model of duopoly?**

The Stackelberg duopoly model refers to the model that lets the dominant firm fix the price first. Later, the follower firms enhance the cost and production. Heinrich Von Stackelberg formed this model in 1934.

**What is the difference between the Stackelberg model vs Cournot?**

In the Stackelberg duopoly model, one firm is the leader and steps up first. The other firms then follow the leader. In comparison, in a Cournot duopoly, firms initiate the move simultaneously.

**What is the Stackelberg model in the supply chain?**

The Stackelberg model in the supply chain is the model that is urged and practiced to get an equilibrium point where the members' profit of the supply chain increases and opt the CSR level in the supply chain. In this model, one must select the supplier as the leader and the manufacturer as the follower.

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