Journal of Optimization Theory and Applications

, Volume 123, Issue 1, pp 163–185

Competitive Advertising Under Uncertainty: A Stochastic Differential Game Approach

  • A. Prasad
  • S. P. Sethi

DOI: 10.1023/B:JOTA.0000043996.62867.20

Cite this article as:
Prasad, A. & Sethi, S.P. Journal of Optimization Theory and Applications (2004) 123: 163. doi:10.1023/B:JOTA.0000043996.62867.20


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.

Advertising dynamic duopoly competitive strategy differential games stochastic differential equations 

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • A. Prasad
    • 1
  • S. P. Sethi
  1. 1.School of ManagementUniversity of Texas at DallasRichardsonTexas

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