The computing in the network (COIN) paradigm has emerged as a potential solution for computation-intensive applications like the metaverse by utilizing unused network resources. The blockchain (BC) guarantees task-offloading privacy, but cost reduction, queueing delays, and redundancy elimination remain open problems. This paper presents a redundancy-aware BC-based approach for the metaverse's partial computation offloading (PCO). Specifically, we formulate a joint BC redundancy factor (BRF) and PCO problem to minimize computation costs, maximize incentives, and meet delay and BC offloading constraints. We proved this problem is NP-hard and transformed it into two subproblems based on their temporal correlation: real-time PCO and Markov decision process-based BRF. We formulated the PCO problem as a multiuser game, proposed a decentralized algorithm for Nash equilibrium under any BC redundancy state, and designed a double deep Q-network-based algorithm for the optimal BRF policy. The BRF strategy is updated periodically based on user computation demand and network status to assist the PCO algorithm. The experimental results suggest that the proposed approach outperforms existing schemes, resulting in a remarkable 47% reduction in cost overhead, delivering approximately 64% higher rewards, and achieving convergence in just a few training episodes.

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