The paper "Cores of Convex Games" by Lloyd S. Shapley explores the core of n-person games, which is the set of feasible outcomes that cannot be improved upon by any coalition of players. A convex game is defined as one based on a convex set function, meaning that the incentives for joining a coalition increase as the coalition grows. The main findings are that the core of a convex game is non-empty and has a regular structure. Additionally, the paper shows that certain cooperative solution concepts, such as the value and the von Neumann-Morgenstern stable set solution, are related to the core in simple ways. Specifically, the value of a convex game is the center of gravity of the extreme points of the core, and the von Neumann-Morgenstern stable set solution of a convex game is unique and coincides with the core. The paper also introduces notation and defines convex games, including their properties and equivalent games.The paper "Cores of Convex Games" by Lloyd S. Shapley explores the core of n-person games, which is the set of feasible outcomes that cannot be improved upon by any coalition of players. A convex game is defined as one based on a convex set function, meaning that the incentives for joining a coalition increase as the coalition grows. The main findings are that the core of a convex game is non-empty and has a regular structure. Additionally, the paper shows that certain cooperative solution concepts, such as the value and the von Neumann-Morgenstern stable set solution, are related to the core in simple ways. Specifically, the value of a convex game is the center of gravity of the extreme points of the core, and the von Neumann-Morgenstern stable set solution of a convex game is unique and coincides with the core. The paper also introduces notation and defines convex games, including their properties and equivalent games.