Price competition in a nonlinear differentiated duopoly

This article represents an attempt to characterise the dynamics of a nonlinear duopoly with price competition and horizontal product differentiation by accounting for non-negativity constraints (on profits and the market demand). The model is set up by following the tradition led by Bischi et al. (1998), according to which players have limited information. The article shows several local and global phenomena of a two-dimensional discrete time system when the price demand elasticity varies. It also points out the differences from both a mathematical and economic point of views in terms of dynamic outcomes when the non-negativity constraints are not binding and when they are binding. This is done by combining mathematical techniques and simulation exercises.