In this paper we model the evolution and interaction between two competing populations as a system of parabolic partial differential equations. The interaction between the two populations is quantified by the presence of non-local terms in the system of equations. We model the whole system as a two-person zero-sum game where the gains accrued by one population necessarily translate into the others loss. For a suitably chosen objective functional(pay-off) we establish and characterize the saddle point of the game. The controls(strategies) are kernels of the interaction terms.
|Number of pages||18|
|Journal||Electronic Journal of Differential Equations|
|Publication status||Published - 13 Dec 1999|
- Game theory
- Optimal control
- Saddle point
ASJC Scopus subject areas