The Function-as-a-Service (FaaS) paradigm has a lot of potential as a computing model for fog environments comprising both cloud and edge nodes, as compute requests can be scheduled across the entire fog contin- uum in a fine-grained manner. When the request rate exceeds capacity limits at the resource-constrained edge, some functions need to be of- floaded towards the cloud. In this paper, we present an auction-inspired approach in which ap- plication developers bid on resources while fog nodes decide locally which functions to execute and which to offload in order to maximize revenue. Unlike many current approaches to function placement in the fog, our ap- proach can work in an online and decentralized manner. We also present our proof-of-concept prototype AuctionWhisk that illustrates how such an approach can be implemented in a real FaaS platform. Through a num- ber of simulation runs and system experiments, we show that revenue for overloaded nodes can be maximized without dropping function requests.