# Advertising a product to face a competitor entry: a differential game approach

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## Abstract

We analyze a market in which advertising is the dominant marketing tool to create market share. We assume that an incumbent firm dominates the market during an initial stage, and that a new competitor is going to enter the market. In particular, we analyze the different advertising policies that the incumbent firm can adopt, before and after the entry of the rival. We explore three possible behaviours. In the first scenario the firm knows that the competitor will arrive at a given instant. In the second one we assume the original firm to be surprised, in the sense that it does not anticipate the entry of the opponent either because it does not expect the competitor to arrive, or it is not prepared to react before the entry takes place. Finally, in the third scenario, the original firm knows that the competitor will enter at a constant rate. We characterize a differential game model and compare the firms’ behaviours in a strategic perspective.

## Keywords

Differential games Nash equilibria Marketing Market entry## JEL Classification

C72 C73 L13 D21## Notes

### Acknowledgements

This work was supported by the University of Padova and the project “Changing market structures in intertemporal optimization” of the Austrian Science Fund (No. P25275-G11). The authors would like to thank the anonymous referees for their valuable remarks and suggestions.

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