As the amount of data generated by the Industrial Internet grows, more and more companies are choosing to outsource the storage for their Industrial Internet data to cloud servers to save storage costs. To prevent the outsourced data from being tampered or deleted, companies need to audit the data integrity regularly. This study proposes a public auditing scheme for Industrial Internet data based on smart contracts. Particularly, a series of game-theory based smart contracts are designed which can efficiently mitigate malicious participators including the third-party auditor and the cloud server. Compared to existing collusion-resistant public auditing schemes, the proposed scheme does not rely on complex cryptographic tools to achieve resistance to participant malicious behavior, and thus is more efficient and suitable to Industrial Internet applications where huge amount of data need to be frequently updated. Specifically, the game-based contract designed in this study as an individual solution, can be effectively combined with existing public auditing schemes to turn out a public auditing scheme with better security without losing efficiency. Finally, a series of tests are conducted on the proposed contract in the local environment and Ropsten, the common test chain for Ethereum. The results show that the designed contract is cheap to run and adaptable to the operating environment, has little impact on the efficiency of the original integrity audit solution, and is more efficient than other integrity schemes that resist the malicious behavior of auditors.