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Analysis of a Lanchester Duopoly

  • Gary M. Erickson
Part of the International Series in Quantitative Marketing book series (ISQM, volume 13)

Abstract

Assume we have two competitors in a competition for market share, and that each wishes to maximize its discounted cash flow over an infinite horizon. We have for competitor 1
$$ \mathop {\max }\limits_{{A_1}} \int\limits_0^\infty {{e^{ - rt}}} ({g_1}M - {A_1})dt $$
(3.1)
and for competitor 2
$$ \mathop {\max }\limits_{{A_2}} \int\limits_0^\infty {{e^{ - rt}}} ({g_2}[1 - M]{A_2})dt $$
(3.2)
The parameters g 1 and g 2 represent the economic values of market shares for competitors 1 and 2, respectively. Also, r is the discount rate, assumed equivalent for the two competitors.

Keywords

Market Share Discount Cash Flow Advertising Strategy Loop Solution Intermediate Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Gary M. Erickson
    • 1
  1. 1.University of WashingtonUSA

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