On functor representation of optimized dynamic multiagent systems

Functors' topoi is chosen as a computational tool for synthesizing dynamic multiagent systems (DMAS). The scale orders the objects as multiagent system states to solve attendant static subgames in them. The initial dynamic game and all static subproblems are represented in the monoidal category of binary relations. Players' preference relations might be maximized in DMAS. The game rational solution is understood as equilibrium. The compositional structure of the optimized DMAS can be described in the form of the game dynamic resulting relation (DRR). Players' rational behavior search is reduced to DRR subsequent maximization. For this purpose, the Bellman's method is generalized to solve control problems stated in the form of relations. The program implementation of the approach can be based on neural networks due to the consistency of the architectures of the applied relation graphs and neural networks.