On a class of games having stable outcomes

One of the most important problems of game theory is the search for conditions for the existence of stable (in one respect or another) outcomes of conflicting situations. In the present note a modification of a class of games having stable outcomes in many respects at once is considered: a minimum is taken as the expression of group interests instead of a maximum. Although the underlying sense of the situation changes completely (now each participant is interested in obtaining the best possible value for any one of the existing indices but not for all of them together), the properties of these classes of games are fairly similar.