The allowable value for cooperative games with restricted permutations

This paper introduces a new framework for cooperative games with restricted permutations, focusing on situations where not all possible player permutations occur. The framework allows players within an ordered coalition to exchange positions if it benefits them. To ensure stable connections among players, we introduce the concept of stably connected ordered coalitions, which incorporates the notions of objection and counter-objection. We then define an order-restricted game, a generalized characteristic function game derived from the original game. Additionally, inspired by the Shapley value, we propose an allowable value and provide its axiomatization. Finally, we explore several extensions of this value to further investigate its potential applications.