A dynamic multi-objective duopoly game with capital accumulation and pollution

Bertrand Crettez, Naila Hayek*, Peter M. Kort

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


This paper studies a discrete-time dynamic duopoly game with homogenous goods. Both firms have to decide on investment where investment increases production capacity so that they are able to put a larger quantity on the market. The downside, however, is that a larger quantity raises pollution. The firms have multiple objectives in the sense that each one maximizes the discounted profit stream and appreciates a clean environment as well. We obtain some surprising results. First, where it is known from the continuous-time differential game literature that firms invest more under a feedback information structure compared to an open-loop one, we detect scenarios where the opposite holds. Second, in a feedback Nash equilibrium, capital stock is more sensitive to environmental appreciation than in the open-loop case.
Original languageEnglish
Article number1983
Number of pages34
Issue number16
Publication statusPublished - Aug 2021


  • game theory
  • corporate environmentalism
  • dynamic multi-objective duopoly
  • open-loop equilibrium
  • feedback Nash equilibrium
  • CSR


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