Stabilization of the Shapley value for cooperative games through level‐induced structures

Abstract Taking into consideration that the Shapley value for cooperative games may not be resistant to potential blocking coalitions, this paper examines the integration of coalition formation and stability in cooperative games. Initially, we establish an endogenous procedure specifically designed for superadditive games. This procedure generates a levels structure and a payoff vector, consequently leading to a modified Shapley value that conforms to the stability notion defined as the levels core. Furthermore, we simulate the procedure in a noncooperative manner and employ the concept of strong Nash equilibrium to demonstrate the stability of the procedure's outcome. Lastly, we propose and delineate a value by applying the same procedural approach to scenarios where the levels structure is predetermined externally.