Mobile Crowdsensing (MCS) is a new paradigm that leverages the collective sensing ability of a crowd so that a special task can be performed through the aggregation of information collected from personal mobile devices. While MCS brings several benefits, its application is prevented by challenges such as the efficient recruitment of users, effective mechanisms for rewarding users to encourage participation, and an effective and fast enough approach for managing the underlying resources that support large-scale MCS applications involving a large number of people in data collection. On the other hand, Artificial Intelligence (AI) applications, which are mostly based on Deep Neural Networks (DNN), are becoming pervasive today and are executed by the end users' mobile devices, which are characterised by limited memory and computing power, and low battery level. This paper describes and evaluates an incentive mechanism for a mobile crowdsensing system with an AI sensing task based on a one-leader multi-follower Stackelberg game. The MCS platform, as a leader, provides an AI sensing task to be executed by a DNN, which can be deployed in two different ways: fully on the user device or partially on the device and partially on edge or cloud resources. The users, as followers, make their decisions regarding their participation to the MCS system and select their desired deployment given the energy and memory available on their device and the deployment reward proposed by the MCS platform. The goals of the MCS platform are: i) to motivate the users to participate in the system, ii) to maximize its profit, and iii) to identify the optimal resources supporting the sensing task that minimizes the cost and provide performance guarantees. This problem has been formulated as a mixed integer nonlinear program and propose an efficient algorithmic approach to solve it quickly. The proposed approach has been compared with some baseline methods and with BARON state-of-the-art solver. Results show that our approach converges to the optimal solution much faster than BARON (up to orders of magnitude) especially in large scale systems. Furthermore, the comparison to the baseline methods shows that our approach always beats the best baseline method under different scenarios providing up to 16% improvement for the MCS platform profit.