What does a dynamic oligopoly maximize? The continuous time Markov case

TL;DR

This paper investigates whether the outcomes of a dynamic oligopoly exploiting a nonrenewable resource can be replicated by a monopoly within a continuous-time Markov framework, providing conditions and explicit solutions.

Contribution

It establishes necessary and sufficient conditions for equivalence and presents explicit solutions, also highlighting cases where monopoly cannot replicate oligopoly outcomes.

Findings

Conditions for oligopoly-monopoly outcome equivalence derived

Explicit solutions provided for specific models

Examples where monopoly cannot replicate oligopoly externalities

Abstract

We analyze the question of whether the outcome of an oligopoly exploiting a nonrenewable resource can be replicated by a related monopoly, within the framework of continuous time and Markov Perfect Nash Equilibrium. We establish necessary and sufficient conditions and find explicit solutions in some cases. Also, very simple models with externalities are shown which Nash equilibrium cannot be replicated in a monopoly.