A lanchester-type dynamic game of advertising and pricing

Steffen Jørgensen, Simon Sigué*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearch

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.

Original languageEnglish
Title of host publicationGames in management science : essays in honor of Georges Zaccour
EditorsPierre-Olivier Pineau, Simon Sigué, Sihem Taboubi
Volume280
Place of PublicationCham
PublisherSpringer Nature Switzerland AG
Publication dateJan 2020
Pages1-14
ISBN (Print)978-3-030-19106-1
ISBN (Electronic)978-3-030-19107-8
DOIs
Publication statusPublished - Jan 2020
SeriesInternational Series in Operations Research and Management Science
Volume280
ISSN0884-8289

Keywords

  • Differential game
  • Duopoly
  • Markovian Nash equilibrium
  • Price and advertising competition

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    Jørgensen, S., & Sigué, S. (2020). A lanchester-type dynamic game of advertising and pricing. In P-O. Pineau, S. Sigué, & S. Taboubi (Eds.), Games in management science: essays in honor of Georges Zaccour (Vol. 280, pp. 1-14). Springer Nature Switzerland AG. International Series in Operations Research and Management Science, Vol.. 280 https://doi.org/10.1007/978-3-030-19107-8_1