# Shapley Machine

In open multi-agent systems where only some agents are controllable, individual value functions previously had no structured basis for learning. Researchers treat the Shapley axioms of efficiency, symmetry and linearity as structural constraints during learning rather than constructing values from the explicit formula, yielding two generic templates, Shapley Machine and Banzhaf Machine. On MPE-PP and SMAC tasks adapted to the n-agent ad hoc teamwork (NAHT) setting, instantiating them on IPPO and POAM generally improved learning efficiency and generalisation to unseen agent types and conventions, though the efficiency axiom weakened generalisation to unseen agent types in some cases.

In open multi-agent systems where only some agents are controllable, individual value functions previously had no structured basis for learning. Researchers treat the Shapley axioms of efficiency, symmetry and linearity as structural constraints during learning rather than constructing values from the explicit formula, yielding two generic templates, Shapley Machine and Banzhaf Machine. On MPE-PP and SMAC tasks adapted to the n-agent ad hoc teamwork (NAHT) setting, instantiating them on IPPO and POAM generally improved learning efficiency and generalisation to unseen agent types and conventions, though the efficiency axiom weakened generalisation to unseen agent types in some cases.