The paper consists of three parts. In the first: “Structure of solutions”, relation (i) of the previous review is proved by a compactness argument. The authors also prove that the essential strategies of one player are precisely those which produce the value of the game in connection with all optimal strategies of the other player. Then it is shown that the set of \(m\times n\) games with unique solutions (\(m\) and \(n\) being fixed) is open and everywhere dense in \(mn\)-space. None of these theorems is generally valid for infinite games. Part II: “Construction of games with given solutions”, produces canonical forms of matrices which have given solution polyhedra satisfying certain necessary conditions (cf. previous review). The latter are thus shown to be sufficient as well. However, it is pointed out that the canonical forms are not promising as a computational aid. Part III: “Solutions of some special games”, deals with completely mixed games and with those whose diagonals exhibit special characteristics.