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A Lanchester-Type Dynamic Game of Advertising and Pricing

  • Steffen Jørgensen
  • Simon SiguéEmail author
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 280)

Abstract

The paper studies a differential game played by two competing firms over a finite time horizon. As the game progresses, the firms observe the position of the game, i.e., the current time and the current market shares. Each firm uses pricing and advertising in order to influence market shares. We suggest a generalization of the Lanchester market share dynamics such that the rates at which firms attract market share from each other are determined not only by their advertising efforts but also by the consumer prices charged in the market. A full characterization of Nash equilibrium price and advertising strategies is obtained.

Keywords

Price and advertising competition Duopoly Differential game Markovian Nash equilibrium 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Business and EconomicsUniversity of Southern DenmarkOdenseDenmark
  2. 2.Faculty of BusinessAthabasca UniversityAthabascaCanada

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