The Internet of Things requires intelligent decision making in many scenarios. To this end, resources available at the individual nodes for sensing or computing, or both, can be leveraged. This results in approaches known as participatory sensing and federated learning, respectively. We investigate the simultaneous implementation of both, through a distributed approach based on empowering local nodes with game theoretic decision making. A global objective of energy minimization is combined with the individual node's optimization of local expenditure for sensing and transmitting data over multiple learning rounds. We present extensive evaluations of this technique, based on both a theoretical framework and experiments in a simulated network scenario with real data. Such a distributed approach can reach a desired level of accuracy for federated learning without a centralized supervision of the data collector. However, depending on the weight attributed to the local costs of the single node, it may also result in a significantly high Price of Anarchy (from 1.28 onwards). Thus, we argue for the need of incentive mechanisms, possibly based on Age of Information of the single nodes.
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