On computation of optimal strategies in oligopolistic markets respecting the cost of change

TL;DR

This paper investigates how to compute equilibrium strategies in oligopolistic markets considering the costs associated with changing production levels, using variational inequalities to analyze stability and applying the theory to dynamic market scenarios.

Contribution

It introduces a variational inequality framework for equilibrium problems with nonsmooth costs and applies it to evolving oligopolistic markets with change costs, including Stackelberg models.

Findings

Lipschitzian stability of the equilibrium characterized

Impact of change costs on market strategies analyzed

Academic examples illustrate theoretical results

Abstract

The paper deals with a class of parametrized equilibrium problems, where the objectives of the players do possess nonsmooth terms. The respective Nash equilibria can be characterized via a parameter-dependent variational inequality of the second kind, whose Lipschitzian stability is thoroughly investigated. This theory is then applied to evolution of a oligopolistic market in which the firms adopt their production strategies to changing input costs, while each change of the production is associated with some "costs of change". We examine both the Cournot-Nash equilibria as well as the two-level case, when one firm decides to take over the role of the Leader (Stackelberg equilibrium). The impact of costs of change is illustrated by academic examples.