Competition among vortex firms: Marketing,R&D or pricing strategy

The mathematical model determines how firms can leverage their advantages to increase their market share. Represented as vortex, firms increase their market scope using: marketing expenses strategy, R&D expenditure strategy or price reduction strategy. For an overpriced good, the R&D strategy is required if sector marketing velocity growth is low otherwise the pricing strategy is suited. Conversely, for an underpriced good, the R&D strategy is used when sector marketing velocity growth is high, but when it is low, the pricing strategy is followed. Distance between firms, competitor marketing velocity and related services share contribute or limit these strategies.