A note: characterizations of convex games by means of population monotonic allocation schemes

Convex cooperative games were first introduced by Shapley (Int J Game Theory 1:11–26, <CitationRef CitationID="CR11">1971</CitationRef>) while population monotonic allocation schemes (PMAS) were subsequently proposed by Sprumont (Games Econ Behav 2:378–394, <CitationRef CitationID="CR13">1990</CitationRef>). In this paper we provide several characterizations of convex games and introduce three new notions: PMAS-extendability, PMAS-exactness, and population monotonic set schemes, which imitate the classical concepts that they extend. We show that all of these notions provide new characterizations of the convexity of the game. Copyright Springer-Verlag Berlin Heidelberg 2014