This paper summarizes the results obtained in connection to the following problems: (A) For a cooperative game in which the Shapley Value is not coalitional rational, find out a new game with the same value, in which the value is coalitional rational. (B) For a cooperative game which is not convex, find out a new game in which the Shapley Value is the same, but the game is convex. (C) The same problems about coalitional rationality and convexity, for two other values, the Egalitarian Allocation and the Egalitarian Nonseparable Contribution, in a new game where these values are unchanged. The convexity threshold and the coalitional rationality thresholds have been introduced and their relationships have been determined. We shall try to discuss the main ideas and give some numerical illustrations.