Order Invariants and the "Environment" Problem for Games with Ordered Outcomes

A property of a game with ordered outcomes is called an order invariant if it does not depend on the addition of unrealizable outcomes. In this paper, some important order invariants are obtained for antagonistic games with ordered outcomes. It is shown that these invariants are connected with equilibrium points in the sense of Nash. For a given game, its so-called majorant extension is constructed so that certain noninvariant properties of the game become its invariants.