Equilibria in a competitive model arising from linear production situations with a common-pool resource

TL;DR

This paper analyzes the strategic behavior of producers competing for a limited common-pool resource in linear production settings, characterizing the structure of Nash equilibria and their subsets.

Contribution

It provides a detailed characterization of pure strategy Nash equilibria, including their relationship with strong and strict Nash equilibria, in a novel competitive model with a common resource.

Findings

Strict Nash equilibria are a subset of strong Nash equilibria.

Strong Nash equilibria form a proper subset of all Nash equilibria.

The model clarifies equilibrium structure in common-pool resource competitions.

Abstract

In this paper we deal with linear production situations in which there is a limited common-pool resource, managed by an external agent. The profit that a producer, or a group of producers, can attain depends on the amount of common-pool resource obtained through a certain procedure. We contemplate a competitive process among the producers or groups of producers and study the corresponding non cooperative games, describing their (strict) Nash equilibria in pure strategies. It is shown that strict Nash equilibria form a subset of strong Nash equilibria, which in turn form a proper subset of Nash equilibria.