  The metaverse, envisioned as the next digital frontier for avatar-based
virtual interaction, involves high-performance models. In this dynamic
environment, users' tasks frequently shift, requiring fast model
personalization despite limited data. This evolution consumes extensive
resources and requires vast data volumes. To address this, meta-learning
emerges as an invaluable tool for metaverse users, with federated meta-learning
(FML), offering even more tailored solutions owing to its adaptive
capabilities. However, the metaverse is characterized by users heterogeneity
with diverse data structures, varied tasks, and uneven sample sizes,
potentially undermining global training outcomes due to statistical difference.
Given this, an urgent need arises for smart coalition formation that accounts
for these disparities. This paper introduces a dual game-theoretic framework
for metaverse services involving meta-learners as workers to manage FML. A
blockchain-based cooperative coalition formation game is crafted, grounded on a
reputation metric, user similarity, and incentives. We also introduce a novel
reputation system based on users' historical contributions and potential
contributions to present tasks, leveraging correlations between past and new
tasks. Finally, a Stackelberg game-based incentive mechanism is presented to
attract reliable workers to participate in meta-learning, minimizing users'
energy costs, increasing payoffs, boosting FML efficacy, and improving
metaverse utility. Results show that our dual game framework outperforms
best-effort, random, and non-uniform clustering schemes - improving training
performance by up to 10%, cutting completion times by as much as 30%, enhancing
metaverse utility by more than 25%, and offering up to 5% boost in training
efficiency over non-blockchain systems, effectively countering misbehaving
users.
