During the last years, researchers have proposed solutions to help smartphones improve execution time and reduce energy consumption by offloading heavy tasks to remote entities. Lately, inspired by the promising results of message forwarding in opportunistic networks, many researchers have proposed strategies for task offloading towards nearby mobile devices, giving birth to the Device-to-Device offloading paradigm. None of these strategies, though, offers any mechanism that considers selfish users and, most importantly, that motivates and defrays the participating devices who spend their resources. In this paper, we address these problems and propose the design of a framework that integrates an incentive scheme and a reputation mechanism. Our proposal follows the principles of the Hidden Market Design approach, which allows users to specify the amount of resources they are willing to sacrifice when participating in the offloading system. The underlying algorithm, that users are not aware of, is based on a truthful auction strategy and a peer-to-peer reputation exchange scheme. Extensive simulations on real traces depict how our designed mechanism achieves higher offloading rate and produces less traffic compared to three benchmark algorithms. Finally, we show how collaborating devices get rewarded for their contribution, while selfish ones get sidelined by others.