Discrete time dynamic oligopolies with adjustment constraints

Chrystie  Burr; Laura  Gardini; Ferenc  Szidarovszky

doi:10.3934/jdg.2015.2.65

Article Contents

2015, Volume 2, Issue 1: 65-87. Doi: 10.3934/jdg.2015.2.65

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Discrete time dynamic oligopolies with adjustment constraints

1.
Department of Economics, University of Colorado, Boulder, CO 80309-0256
2.
Department of Economics, Society, Politics, Università degli Studi di Urbino, 61029 Urbino
3.
Department of Applied Mathematics, University of Pécs, Pécs, 7624

Received: October 2014

Revised: March 2015

Published: January 2015

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Abstract

A classical $n$-firm oligopoly is considered first with linear demand and cost functions which has a unique equilibrium. We then assume that the output levels of the firms are bounded in a sense that they are unwilling to make small changes, the output levels are bounded from above, and if the optimal output level is very small then the firms quit producing, which are realistic assumptions in real economies. In the first part of the paper, the best responses of the firms are determined and the existence of infinitely many equilibria is verified. The second part of the paper examines the global dynamics of the duopoly version of the game. In particular we study the stability of the system, the bifurcations which can occur and the basins of attraction of the existing attracting sets, as a function of the speed of adjustment parameter.

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Mathematics Subject Classification: Primary: 91A06, 91A25, 91A50, 91B55; Secondary: 37G35, 37G15.

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