Cooperative games with size-truncated information

We study the marginal worth vectors and their convex hull, the so-called Weber set, from the original coalitional game and the transformed one, which is called the Weber set of level k. We prove that the core of the original game is included in each of the Weber set of level k,for any k,and that the Weber sets of consecutive levels form a chain if and onlyif the original game is 0-monotone. Even if the game is not 0-monotone, theintersection of the Weber sets for consecutive levels is always not empty, what is not the case for non-consecutive ones.