Games with exhaustible resources

Chris Harris, Sam Howison, Ronnie Sircar

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


We study N-player continuous-time Cournot games in an oligopoly where firms choose production quantities. These are nonzero-sum differential games, whose value functions may be characterized by systems of nonlinear Hamilton-Jacobi PDEs. When resources such as oil are in finite supply, exhaustibility enters as a boundary condition for the PDEs. We analyze the problem when there is an alternative, but expensive, technology (for example, solar power for energy production) and give an asymptotic approximation in the limit of small exhaustibility. We illustrate the two-player problem by numerical solutions and discuss the impact of limited oil reserves on production and oil prices in the duopoly case.

Original languageEnglish (US)
Pages (from-to)2556-2581
Number of pages26
JournalSIAM Journal on Applied Mathematics
Issue number7
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


  • Differential games
  • Exhaustible resources
  • Game theory
  • Nonlinear partial differential equations


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