Mastering multi-player games

We consider multi-player games, and the guarantees that a master player that plays on behalf of a set of players can offer them, without making any assumptions on the rationality of the other players. Our model consists of an (n + 1)-player game, withm strategies per player, in which a master player M forms a coalition with nontransferable utilities among n players, and the remaining player is called the independent player. Existentially, it is shown that every game admits a product-minimax-safe strategy for M — a strategy that guarantees for every player in M ’s coalition an expected value of at least her product minimax value (which is at least as high as her minimax value and is often higher). Al-gorithmically, for any given vector of values for the players, one can decide in polytime whether it can be ensured b