Multi-market Oligopoly of Equal Capacity

TL;DR

This paper analyzes a multi-market Cournot competition model with equal capacity firms, proving the existence and stability of a unique symmetric Nash equilibrium, and discusses its implications in transportation networks.

Contribution

It introduces a novel analysis of a multi-market Cournot model with equal capacities, establishing equilibrium properties and stability, with applications to transportation.

Findings

Unique symmetric Nash equilibrium exists

Equilibrium characterized by a potential function maximum

Equilibrium is globally asymptotically stable

Abstract

We consider a variant of Cournot competition, where multiple firms allocate the same amount of resource across multiple markets. We prove that the game has a unique pure-strategy Nash equilibrium (NE), which is symmetric and is characterized by the maximal point of a "potential function". The NE is globally asymptotically stable under the gradient adjustment process, and is not socially optimal in general. An application is in transportation, where drivers allocate time over a street network.