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

See all articles by Ashutosh Prasad

Ashutosh Prasad

University of California, Riverside (UCR)

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

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

Prasad, Ashutosh and Sethi, Suresh, Competitive Advertising Under Uncertainty: A Stochastic Differential Game Approach (August 1, 2003). Journal of Optimization Theory and Applications, Vol. 123, No. 1, pp. 163-185, October 2004, Available at SSRN: https://ssrn.com/abstract=440621 or http://dx.doi.org/10.2139/ssrn.440621

Ashutosh Prasad (Contact Author)

University of California, Riverside (UCR)

900 University Avenue
Riverside, CA CA 92521
United States

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

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