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By Vladimir Mazalov, Dmitry Novikov, Guennady Ougolnitsky, Leon Petrosjan

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The increase by 100  i percent). In this case, the coordinated planning problem acquires the form F  F1 ; F1 ; ... ; Fm   max (2) subject to the constraints Fi  1   i Fi 0 , i  1, n . (3) PROBLEM STATEMENT There are n candidate projects for inclusion in the program. Implementation of each project iincurs the costs ci and yields the economic effect aij for direction j (we comprehend effect as the increment of the goal function Fj). Set xi = 1 if project iis included in the program (xi = 0, otherwise).

Nikitina, Guennady A. Ougolnitsky et al. to fishery. Therefore, it is necessary to develop the mathematical models of fish kills prevention in shallow waterbodies, as well as to elaborate scientifically substantiated suggestions on fish kills prevention. For instance, we mention the books [1, 4, 13] in the former field of research and the series of papers [5, 17, 18, 21, 22] dedicated to the latter field. In contrast to these works, the present paper performs analysis based on the gametheoretic approach [3, 7 – 9, 11].

At any instant and any point of the spatial domain, the optimal strategy of the supervisor is defined by if a / b, u * ( x, y, z, t )    q( x, y, z, t ), a / b  q( x, y, z, t ), otherwise. And the equilibrium pair (q*,u*) (the corresponding strategies of the supervisor and agent) has the form P( x, y, z, t ), P( x, y, z, t ) , if P( x, y, z, t )  a / b, (q* , u * )   P( x, y, z, t ), a / b), otherwise.  Within the framework of Germeier game Г2x, at any instant and any point of the spatial domain the penalty strategy applied by the supervisor to the agent is qP(x,y,z,t) = 0 for ( x, y, z )  G .

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