Agent games and agency games

Non-cooperative games are considered, in which the payoff functions of some players depend on the actions of only a part of the entire set of players. A method for constructing a non-cooperative game with a smaller number of players for games with a larger number of players is proposed. The participants of the new game will be administrators of coalitions of players, whose payoffs are not affected by the actions of other players from this coalition. Examples of creating coalitions, the capabilities of the administrator with a correctly assigned fee are listed. For special cases, it is possible to define mixed strategies of the administrator, consistent with mixed strategies of the players.