New paper from Ryzák & Kroupa: tractable cooperative games on directed networks with closed-form Shapley value

Ryzák and Kroupa's paper presents a new class of cooperative games induced by weighted directed networks. In these games, the value of a coalition depends on two components: an internal interaction term from the induced subgraph (the network among coalition members) and an external component based on the minimal weight of incoming edges from nodes outside the coalition. This structure mirrors real-world scenarios like supply chains, influence networks, or resource allocation where both internal and external ties matter.

The key theoretical contribution is a representation in terms of unanimity games, which leads to closed-form polynomial-time formulas for the Shapley value and the Banzhaf value — classic fairness-based allocation rules. Additionally, the authors show the game has a nonempty core and is totally balanced, meaning stable allocations exist. Crucially, the class reveals a separation between stability-based (core) and fairness-based (Shapley) solutions, a rare property in tractable models. This makes it a valuable framework for network economics, AI fairness, and multi-agent systems where both efficiency and equity matter.