The flow game with public arcs is a cooperative revenue game derived from a flow network. In this game, each player possesses an arc, while certain arcs, known as public arcs, are not owned by any specific player and are accessible to any coalition. The aim of this game is to maximize the flow that can be routed in the network through strategic coalition formation. By exploring its connection to the maximum partially disjoint path problem, we investigate the approximate core and nucleon of the flow game with public arcs. The approximate core is an extension of the core that allows for some deviation in group rationality, while the nucleon is a multiplicative analogue of the nucleolus. In this paper, we provide two complete characterizations for the optimal approximate core and show that the nucleon can be computed in polynomial time.

翻译：公共弧流博弈是一种基于流网络的合作收益博弈。在该博弈中，每个玩家拥有一条弧，而某些被称为公共弧的弧不属于任何特定玩家，任何联盟均可使用。该博弈的目标是通过战略联盟形成最大化网络中的可路由流量。通过探索其与最大部分不相交路径问题的联系，我们研究了公共弧流博弈的近似核和核子。近似核是核的扩展，允许群体理性存在一定偏差，而核子是核仁的乘法模拟。本文给出了最优近似核的两种完整刻画，并证明核子可在多项式时间内计算。