Prehistory graph of the move of a player in multistage games with separated dynamics

Analysis of information structure of multistage games with separated dynamics, with a player set of arbitrary cardinality, in which information of the player about the process is determined by means of his vector-function, is given in the paper. The definition of a prehistory graph of the move of a player to analyze information solvability of an ordered according to the players set of information vector-functions is introduced. Necessary and sufficient conditions theorems of information solvability in the language of graphs of move prehistories for multistage games both with a finite and infinite set of players are obtained. The impact of the graph of move prehistory cycles on information solvability is separately investigated. All the basic theorems and statements are accompanied with examples illustrating them.