Function-as-a-Service (FaaS) is a programming model in which applications are formed by chaining ephemeral computation units referred to as functions. FaaS is particularly suitable for developing fog-native applications by enabling flexible, on-demand placement of functions across the cloud-to-thing continuum. This continuum encompasses diverse fog nodes ranging from cloud servers to myriads of resource-constrained and geographically-distributed devices. Although many recent studies have focused on efficiently placing functions on fog resources, limited attention has been given to respecting application latency requirements. Moreover, few studies have considered the multiple entities that own fog nodes and explored mechanisms to incentivize fog node owners to share resources within the same fog network to improve quality of service for clients. This paper addresses the FaaS function placement problem in the fog through a market-based approach. Clients submit function placement requests with expected guarantees over network latency and allocated resources, encapsulated within a Service-Level Agreement (SLA). A marketplace then organizes an auction where fog nodes bid on the SLA to determine the node that will host the function and the revenue of the fog node owner. Our approach is evaluated by emulating networks of fog nodes, utilizing our reproducible and open-source testbed running on the Grid’5000 infrastructure. We evaluate various cooperative baselines on the same testbed and demonstrate that our approach reduces client spending by 70% while maintaining the expected latency across fog networks with up to 663 nodes, under realistic loads from FaaS function chains.