Analysis of a Lanchester Duopoly

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


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
$$ \mathop {\max }\limits_{{A_1}} \int\limits_0^\infty {{e^{ - rt}}} ({g_1}M - {A_1})dt $$
and for competitor 2
$$ \mathop {\max }\limits_{{A_2}} \int\limits_0^\infty {{e^{ - rt}}} ({g_2}[1 - M]{A_2})dt $$
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.


Market Share Discount Cash Flow Advertising Strategy Loop Solution Intermediate Interval 
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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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