A stochastic differential game of duopolistic competition with sticky prices

Luca Colombo, Paola Labrecciosa

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Abstract

In this paper, we present a stochastic differential game model of duopolistic competition with sticky prices, which extends the model analyzed in the seminal paper by Fershtman and Kamien (1987), and derive analytically a feedback Nash equilibrium of the game. Uncertainty is modelled by means of a Wiener process affecting the evolution of the price. We show that the expected price converges to a level that can be either higher or lower than the deterministic stationary price, depending on market size. We also show that uncertainty is beneficial to firms in terms of long-run expected profits and may be beneficial to firms in terms of discounted expected profits, depending on market size as well. Furthermore, we show that the long-run stationary probability density of the market price can be computed explicitly.

Original languageEnglish
Article number104030
Number of pages16
JournalJournal of Economic Dynamics and Control
Volume122
DOIs
Publication statusPublished - Jan 2021

Keywords

  • Cournot competition
  • Markov Perfect Equilibrium
  • Oligopoly
  • Sticky prices
  • Stochastic differential games

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