Lanchester games have their origin in the work of F.W. Lanchester: Aircraft in Warfare: The Dawn of the Fourth Arm (Constable, London, UK, 1916) who used ordinary differential equations to represent stylized problems of military combat. Later on, one of Lanchester’s models – with a straightforward reinterpretation - has been used to describe the effects of advertising competition for market share (or sales) in oligopolistic markets. In particular, there is a stream of literature in which the Lanchester dynamics have been used as a component of a differential game.
I present a simple dynamic advertising game model, cast as a differential game with Lanchester dynamics and show how this game has been extended in various directions. Furthermore, I present a new approach to Lanchester games, having connections to the economic theory of contests.
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