The profitability of small horizontal mergers with nonlinear demand functions

We want to take a differential game approach with price dynamics to conduct an investigation into the consequences of horizontal merger of firms where the demand function is nonlinear. We take into consideration the open-loop equilibrium. We show that in relation to the fact that the demand is nonlinear and prices follow some stickiness an incentive for small merger exists, while it does not appear under the standard approach using a linear demand function.