The present paper examines a modification of the game with unopposed interests first stated and solved in [ll. Our statement of the game differs from that in [II in just one respect: it is assumed that the first player does not know precisely the second player’s pay-off function, he only knows its range of variation, i.e. he has information on the functions fi’(x,, x2), fz+(Xl, x2), where f,+ (x1, x,) >/f2(xI, x2) >/f2-(x,, x,); the functions f,, fi’ and f2+ are assumed continuous, while x1 and x, belong to compacta X, and X,. AS in [II, therefore, the first player, counting on his information on the concrete choice of the second player 1c, s X,, chooses his strategy x,(x,> and communicates it to the second player. The final choice of strategy x,(x2) is fully determined by the first player’s attempt to ensure himself under these conditions the best guaranteed result, starting from the pay-off function fi(x,, n,). The second player’s behaviour is fully described by his attempt to increase his pay-off function f2(xl, x,) (not exactly known to the first player), by selecting x, E X,, knowing the function x1(x,).