Experts Work Together: Learning MoE Routing from Cooperative Games

MoE models select a small number of experts for each token, and an expert's contribution depends on which experts are activated together. We model MoE expert interactions through cooperative games: under a fixed Top-k constraint, we treat two compatible expert replacement actions as players and define coalition utility as the loss reduction of a complete expert combination relative to natural routing. Marginal contributions and the pairwise interaction identify complementarity and conflict missed by per-action evaluation. We then propose GameMoE, which constructs an interaction-weighted reward from coalition utilities. Router updates account for single-action utility and pairwise interaction, with the interaction scaled by the other replacement's current selection probability. Training combines this coalition supervision with cross-entropy on the natural forward pass and constrains relative routing score changes among experts with respect to the initial router; inference keeps the native Top-k without search or utility evaluation. Theoretical analysis characterizes how loss curvature gives rise to interactions and how they enter routing updates. GameMoE achieves the best greedy-decoding results among the evaluated methods on social commonsense reasoning and both multi-hop and single-paragraph reading comprehension. These results support using cooperative games to guide expert selection and make better use of existing expert capacity under a fixed activation budget.