Optimal Pricing and Advertising in a Durable-Good Duopoly
European Journal of Operational Research, Vol. 200, No. 2, pp. 486-497, January 2010
33 Pages Posted: 2 Apr 2008 Last revised: 28 May 2010
Date Written: January 1, 2009
This paper analyzes dynamic advertising and pricing policies in a durable-good duopoly. The proposed infinite-horizon model, while general enough to capture dynamic price and advertising interactions in a competitive setting, also permits closed-form solutions. We use differential game theory to analyze two different demand specifications - linear demand and isoelastic demand - for symmetric and asymmetric competitors. We find that the optimal price is constant and does not vary with cumulative sales, while the optimal advertising is decreasing with cumulative sales. Comparative statics for the results are presented.
Keywords: Optimal Control, Dynamic programming, Game theory, Differential games, Pricing, Advertising, Nash equilibrium, the Sethi model, Durable goods, Innovative products
JEL Classification: M3, M31, M37, C71, C73, D4
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