Oligopoly dynamics with isoelastic demand: The joint effects of market saturation and strategic delegation

Abstract

In the framework of a Cournot oligopoly game with isoelastic demand, we examine the simultaneous presence of both market saturation and strategic delegation. Although these two (realistic) aspects have already been considered in the literature each on its own, we aim at deepening their joint interactions when matched together in oligopolistic competition. In addition, we admit the possibility that delegation activities actuated by firms to weaken or even exclude competitors from the market may cease if undertaken by successful players, which thus regain their pure profit maximizing behavior. In this context, a limited market saturation level (positively) influences the effectiveness of delegation strategies and, at the same time, can sustain equilibrium configurations for the winning (monopolistic) firm even under the isoelastic market structure. Through local stability analysis, we show how the combination of strategic delegation with market saturation contributes to determine the equilibrium number of active players and the local asymptotic stability of the (economically relevant) equilibrium. Moreover, non-equilibrium dynamics reveal the presence of periodic cycles along which a firm is active while its competitors alternatively exits and enters the market. We show why these interesting scenarios are due to the joint interplay between strategic delegation and market saturation.