Group for Research in Decision Analysis

Recent developments in differential games of advertising with Lanchester dynamics

Steffen Jørgensen University of Southern Denmark, Denmark

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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