Decentralized P2P networks have emerged as robust instruments to execute computing tasks, with enhanced security and transparency. Solutions such as Blockchain have proved to be successful in a large catalog of critical applications such as cryptocurrency, intellectual property, etc. However, although executions are transparent and P2P are resistant against common cyberattacks, they tend to be untrustworthy. P2P nodes typically do not offer any evidence about the quality of their resolution of the delegated computing tasks, so trustworthiness of results is threatened. To mitigate this challenge, in usual P2P networks, many different replicas of the same computing task are delegated to different nodes. The final result is the one most nodes reached. But this approach is very resource consuming, especially in terms of energy, as many unnecessary computing tasks are executed. Therefore, new solutions to achieve trustworthy P2P networks, but with an energy efficiency perspective, are needed. This study addresses this challenge. The purpose of the research is to evaluate the effectiveness of an audit-based and score-based approach is assigned to each node instead of performing identical tasks redundantly on different nodes in the network. The proposed solution employs probabilistic methods to detect the malicious nodes taking into account parameters like number of executed tasks and number of audited ones giving a value to the node, and game theory which consider that all nodes play with the same rules. Qualitative and quantitative experimental methods are used to evaluate its impact. The results reveal a significant reduction in network energy consumption, minimum a 50% comparing to networks in which each task is delivered to different nodes considering the task is delivered to a pair of nodes, supporting the effectiveness of the proposed approach.