We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas five player game with a unique stable set different from the core,...

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...</citationref></citationref>

The existence of von Neumann–Morgenstern solutions (stable sets) for assignment games has been an unsolved question since Shapley and Shubik (1972) [11]. For each optimal matching between buyers and sellers, Shubik (1984) [12] proposed considering the union of the core of the game and the core...

An assignment game is defined by a matrix A, where each row represents a buyer and each column a seller. If buyer i is matched with seller j, the market produces aij units of utility. We study Monge assignment games, that is bilateral cooperative assignment games where the assignment matrix...