Complexity in a Duopoly Game with Homogeneous Players, Convex, Log-linear Demand and Quadratic Cost Functions

In this study we investigate the dynamics of a nonlinear discrete-time duopoly game, where the players have homogeneous expectations. We suppose that the cost function is quadratic and the demand is a convex and log- linear function. 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.