BeliefMerge: Bayesian Game Theoretic Model Merging with Joint Beliefs

Model merging combines multiple task-specific models fine-tuned from a shared base model into a single model with consolidated capabilities. Yet, model merging is inherently uncertain because each task-specific model cannot directly observe the private characteristics of others, making contribution coordination difficult. Existing methods typically rely on public model information or locally available task information without explicitly accounting for such uncertainty. To address this issue, we introduce BeliefMerge, a Bayesian game-theoretic framework for uncertainty-aware model merging. BeliefMerge constructs correlated joint beliefs over unobserved model characteristics and coordinates interdependent contributions via a Bayesian Nash Equilibrium. Theoretically, sufficient conditions are established for equilibrium uniqueness and convergence of exact best-response updates. Experiments across CLIP and GLUE show that BeliefMerge achieves the best performance on all nine CLIP configurations and five of eight GLUE tasks, demonstrating its empirical superiority.