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A Linear State Game of Advertising à la Vidale-Wolfe

Author

Listed:
  • Luca Lambertini

    (University of Bologna)

  • Andrea Mantovani

    (Operations and Management Sciences, TBS Business School)

Abstract

We revisit the tradition of advertising models stemming from Vidale and Wolfe (Oper Res 5:370–381;1957) to illustrate the possibility of building up a game delivering a (degenerate) feedback equilibrium under open-loop rules. To this aim, we reformulate the state equation of the generic firm in such a way that its own advertising effort and the rivals’ reaction to it enter the state dynamics additively. This approach amounts to envisaging situations where advertising has an essentially predatory/defensive nature, as it is not designed to modify the natural growth rate of a firm’s sales or market share. This modeling strategy gives the game a state-linear structure, which also delivers an Arrovian result concerning the relationship between the aggregate advertising effort and industry structure.

Suggested Citation

  • Luca Lambertini & Andrea Mantovani, 2025. "A Linear State Game of Advertising à la Vidale-Wolfe," International Series in Operations Research & Management Science,, Springer.
    • Handle: RePEc:spr:isochp:978-3-031-88638-6_6
    DOI: 10.1007/978-3-031-88638-6_6
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