Ronnie Sircar
Games with Exhaustible Resources
We study N-player repeated Cournot competitions that model the
determination of price in an oligopoly where firms choose quantities.
These are nonzero-sum (ordinary and stochastic) differential games,
whose value functions may be characterized by systems of nonlinear
Hamilton-Jacobi-Bellman partial differential equations. When the
quantity being produced is in finite supply, such as oil,
exhaustibility enters as boundary conditions for the PDEs. We analyze
the problem when there is an alternative, but expensive, resource (for
example solar technology 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 dupoly case.
Joint work with Chris Harris (Cambridge University) and Sam Howison
(Oxford University).