Short- and long-term optimality under sustainable threats in Contest Theory models of advertising and short-run competition

Reinoud A.M.G. Joosten*, Rogier Harmelink, Thom Sparrius

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

We model advertising with effects on different time scales for a duopoly in imperfect substitutes using elements from Contest Theory. Firms additionally compete in a short-run strategic variable, here price or quantity, allowing simultaneous or sequential decisions, or collusion in endogenously changing stage games. Strategic variables range from ‘slow’ (advertising), over ‘moderate’ (quantities) to ‘fast’ (prices). We find feasible rewards and equilibria for the limiting average reward criterion. Uniqueness of equilibrium is not guaranteed, and we introduce two criteria which act as natural refinements. We impose stage-game rationality, i.e., the firms play optimally in each stage game. Furthermore, in establishing threats, we require that punishment is sustainable, i.e., the punisher must have nonnegative long term average own profits to avoid bankruptcy.
Original languageEnglish
JournalAnnals of operations research
DOIs
Publication statusE-pub ahead of print/First online - 13 Jan 2025

Keywords

  • UT-Hybrid-D
  • externalities
  • limiting average rewards
  • equilibria
  • long-term and stage-game optimality
  • sustainable threats
  • advertising

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