# Cournot’s Oligopoly Equilibrium under Different Expectations and Differentiated Production

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Underlying Theory and General Assumptions

**Assumption 1.**

- -
- The three products are not too different from each other in terms of quality and/or
- -
- The products are not extremely substitutable for each other.

**Assumption 2.**Firms have linear cost functions with a zero constant, i.e., their marginal costs ($M{C}_{k}$, $k=1,2,3$) are constant for any quantity of output. To exclude negative output, rule$M{C}_{k}>0$and${\alpha}_{k}-M{C}_{k}>0,k=1,2,3$was applied. The second inequality represents the net quality of the firm’s output [7].

#### 1.2. Cournot Oligopoly Model

#### 1.3. Adaptation Possibilities of Oligopolists over Time

## 2. Proposed Model Modifications

_{i}.

#### 2.1. Cartel Oligopoly Model

#### 2.2. Naïve, Adaptive, and Real Expectations

#### 2.2.1. Naïve Expectations

#### 2.2.2. Adaptive Expectations

#### 2.2.3. Real Expectation

## 3. Results

_{2}), so the model could be applied. In this case, the exogenous variables are based on data published in the annual reports of the mobile operators Slovak Telecom [40], O

_{2}[41], and in the case of Orange are based on data published in Finstat [42].

#### 3.1. Naïve Expectations

#### 3.2. Adaptive Expectations

#### 3.3. Real Expectations

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Maximum Lyapunov exponent for adaptive expectations and $\gamma =\left(-0.978;-0.711\right)$.

**Figure 5.**Adjustment coefficient changing: (

**a**) maximum Lyapunov exponent for ${\mu}_{3}=\left(0.337;0.369\right)$; (

**b**) bifurcation diagram for quantity of the 1st firm when ${\mu}_{3}=\left(0.3;0.369\right)$.

Company | ARPU $\left({\mathit{\alpha}}_{\mathit{i}}\right)$ | Marginal Cost $\left(\mathit{M}{\mathit{C}}_{\mathit{i}}\right)$ | Coefficient of Adjustment (μ _{i}) |
---|---|---|---|

1st company (Orange Slovakia) | 15.80 | 0.166 | 0.20 |

2nd company (Slovak Telecom) | 12.90 | 0.177 | 0.15 |

3rd company (0_{2}) | 10.90 | 0.106 | 0.20 |

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Grisáková, N.; Štetka, P.
Cournot’s Oligopoly Equilibrium under Different Expectations and Differentiated Production. *Games* **2022**, *13*, 82.
https://doi.org/10.3390/g13060082

**AMA Style**

Grisáková N, Štetka P.
Cournot’s Oligopoly Equilibrium under Different Expectations and Differentiated Production. *Games*. 2022; 13(6):82.
https://doi.org/10.3390/g13060082

**Chicago/Turabian Style**

Grisáková, Nora, and Peter Štetka.
2022. "Cournot’s Oligopoly Equilibrium under Different Expectations and Differentiated Production" *Games* 13, no. 6: 82.
https://doi.org/10.3390/g13060082