Electron. J. Diff. Eqns., Vol. 1999(1999), No. 50, pp. 1-18.

A minmax problem for parabolic systems with competitive interactions

Sanjay Chawla

Abstract:
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.

Submitted June 16, 1999. Published December 13, 1999.
Math Subject Classifications: 49K35, 49K20, 49K22, 35K57, 45K05.
Key Words: optimal control, game theory, saddle point.

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Sanjay Chawla
Department of Computer Science
University of Minnesota
Minneapolis, MN 55455 USA
e-mail: chawla@cs.umn.edu

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