Multiplayers' games compositional structure in the monoidal category of binary relations

The system approach is suggested for multiplayers' games solution that meets up-to-date network technologies. It allows to optimize the functionality of multiagent systems. The monoidal category of binery relations is applied to make games rules description and players' behavior study and modification. The game problem is to maximize, if possible, the preference relations of all participants in the game. Their composition in the monoidal binary relations category in correspondence with games rules defines resulting game relation (RGR). Players' rational behavior search is reduced to RGR maximum elements choice. The author formalizes the use of various classes of permissible strategies, information exchange processes, and coalitions formation. The RGR existence is proved and maximum RGR elements structure is studied. Moves priority and absolutely optimal preference relations significance are clarified for the coalitions formation process.