A Minmax Problem for Parabolic Systems with Competitive Interactions
Date
1999-12-13
Authors
Chawla, Sanjay
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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.
Description
Keywords
Optimal control, Game theory, Saddle point
Citation
Chawla, S. (1999). A minmax problem for parabolic systems with competitive interactions. <i>Electronic Journal of Differential Equations, 1999</i>(50), pp. 1-18.
Rights
Attribution 4.0 International