Minimum-effort games, communication networks, and the Myerson value

This paper proposes a cooperative approach to minimum-effort games on networks. In line with the coordination game literature, we consider environments in which production is determined by the lowest effort among active agents. Rather than focusing on strategic effort choices, we examine how the resulting utility should be fairly allocated ex post. To address this question, we introduce a framework of multi-choice games in which agents can contribute at different effort levels within coalitions and interact through a communication network. Cooperation is constrained in two ways: minimum-effort requirements force coalition members to match the effort of the least active participant, while network restrictions limit cooperation to connected groups of agents. We first define the class of cooperative minimum-effort games as a linear subspace of multi-choice games and derive a basis for this space. We then combine minimum-effort and network constraints into a restricted game and propose a corresponding extension of the Myerson value. Finally, we provide an axiomatic characterization of this value using both classical and novel axioms, including Second-Order Fairness, inspired by the double-differences method in statistics.