Competitive Advertising Under Uncertainty: A Stochastic Differential Game Approach
Journal of Optimization Theory and Applications, Vol. 123, No. 1, pp. 163-185, October 2004
45 Pages Posted: 9 Dec 2003 Last revised: 13 May 2009
Date Written: August 1, 2003
Abstract
We analyze optimal advertising spending in a duopolistic market where each firm's market share depends on its own and its competitor''s advertising decisions, and is also subject to stochastic disturbances. We develop a differential game model of advertising in which the dynamic behavior is based on the Sethi stochastic advertising model and the Lanchester model of combat. Particularly important to note is the morphing of the sales decay term in the Sethi model into decay caused by competitive advertising and noncompetitive churn that acts to equalize market shares in the absence of advertising. We derive closed-loop Nash equilibria for symmetric as well as asymmetric competitors. For all cases, explicit solutions and comparative statics are presented.
Keywords: Advertising, advertising budgeting, competitive strategy, stochastic differential game, stochastic calculus, duopoly, stochastic differential equations, Ito equations, dynamic programming, the Sethi model, Nash equilibrium
JEL Classification: C61, M3, M31, M37, M31, M00, C72, C73
Suggested Citation: Suggested Citation
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