# Conditions for stable equilibrium in Cournot duopoly models with tax evasion and time delay

## TL;DR

This paper establishes conditions ensuring stable and delay-independent equilibrium in Cournot duopoly models that incorporate tax evasion and time delays, with specific assumptions on costs and evasion probabilities.

## Contribution

It provides novel stability conditions for Cournot models with tax evasion and delays, including economic interpretations and examples satisfying these conditions.

## Key findings

- Conditions imply asymptotic stability and delay independence.
- Equal marginal costs and evasion probabilities are key assumptions.
- Examples demonstrate the applicability of the conditions.

## Abstract

We provide conditions for stable equilibrium in Cournot duopoly models with tax evasion and time delay. We prove that our conditions actually imply asymptotically stable equilibrium and delay independence. Conditions include the same marginal cost and equal probability for evading taxes. We give examples of cost and inverse demand functions satisfying the proposed conditions. Some economic interpretations of our results are also included.