Large language model (LLM)-based multi-agent systems (MAS) predominantly rely on centralized orchestration and lack formal verification mechanisms for agent reliability, participation, and system-level behavioral alignment. These shortcomings leave open environments severely vulnerable to uncooperative or malicious agents. This work proposes DART, a Directed Acyclic Graph (DAG)-based reputation and incentive regulation framework for trustworthy multi-agent collaboration, combining centralized operational orchestration with blockchain-enabled decentralized governance and accountability. DART unifies DAG workflow orchestration, capability and reputation-aware task allocation, dynamic behavior updates, multi-factor incentives, and smart contract accountability paired with IPFS storage. Under this paradigm, agent selection dynamically balances task alignment, historical reputation, and workload, while post-execution behavioral evidence continuously calibrates agent trust and the probability of future participation. Evaluated across four axes, DART achieves 93.6% Pass@1 on GSM8K and builds a full-stack application in 142 s using two agents, outperforming centralized baselines. Across five independent 150-round longitudinal trials, Full DART achieves a mean task success rate of 93.33 +/- 2.26%, output quality of 0.9357 +/- 0.0117, retry rate of 0.2307 +/- 0.0816, and allocation delay of 1.1153 +/- 0.0408 s, consistently outperforming its ablated configurations DART isolates persistent and intermittent malicious agents, obtaining a 99.3% output containment rate and restoring system success to 99.8%. These results demonstrate the potential of coupling reputation, incentives, DAG-based coordination, and verifiable blockchain-enabled governance to support adaptive and accountable multi-agent collaboration.

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