Article

 

ON A DUOPOLY GAME WITH HOMOGENEOUS PLAYERS AND A QUADRATIC DEMAND FUNCTION (p.39-48)

by

Georges Sarafopoulos, DEMOCRITUS UNIVERSITY OF THRACE

Keywords : Cournot duopoly game; Discrete dynamical system; Homogeneous expectations; Stability; Chaotic Behavior

JEL classification : C62, C72, D43

Abstract

In this study we investigate the dynamics of a nonlinear discrete-time duopoly game, where the players have homogeneous expectations. We suppose that the demand is a quadratic function and the cost function is linear. The game is modeled with a system of two difference equations. Existence and stability of equilibria of this system are studied. We show that the model gives more complex chaotic and unpredictable trajectories as a consequence of change in the speed of adjustment of the players. If this parameter is varied, the stability of Nash equilibrium is lost through period doubling bifurcations. The chaotic features are justified numerically via computing Lyapunov numbers and sensitive dependence on initial conditions.