A Linear State Game of Advertising à la Vidale-Wolfe

Luca Lambertini () and Andrea Mantovani ()
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Luca Lambertini: University of Bologna
Andrea Mantovani: Operations and Management Sciences, TBS Business School

Chapter Chapter 6 in The Unaffordable Price of Static Decision-making Models, 2025, pp 81-93 from Springer

Abstract: 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.

Keywords: Advertising; Oligopoly; Differential games; Strong time consistency; C73; L13; M37 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-3-031-88638-6_6

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DOI: 10.1007/978-3-031-88638-6_6

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