A Comparison of the Myerson Value and the Position Value

In the realm of graph-restricted games, the underlying network structure plays a pivotal role, enforcing a key constraint: communication between agents is only feasible if a valid path connecting them exists within the network. This constraint significantly influences the dynamics and strategies, particularly in value allocation scenarios among connected agents. Among various contributions to the allocation rules for such network-centric scenarios, Myerson's pioneering work stands out [4, 5]. Named after him, the Myerson value represents an adaptation of the Shapley value [7]. Another prominent concept in this domain is the position value [1, 6]. Both serve as solution concepts, offering distinct perspectives, with the Myerson value focusing on agents and the position value on links between agents. We provide an axiomatic characterization of the Myerson value based on two fundamental axioms. Expanding our investigation, a subtle modification of the first axiom leads to a characterization of the position value. This extension enables comparing these value operators, highlighting their essential distinctions and similarities.