Recently, coded distributed computing (CDC), with advantages in intensive computation and reduced latency, has attracted a lot of research interest for edge computing, in particular, IoT applications, including IoT data pre-processing and data analytics. Nevertheless, it can be challenging for edge infrastructure providers (EIPs) with limited edge resources to support IoT applications performed in a CDC approach in edge networks, given the additional computational resources required by CDC. In this paper, we propose coded edge federation, in which different EIPs collaboratively provide edge resources for CDC tasks. To study the Nash equilibrium, when no EIP has an incentive to unilaterally alter its decision on edge resource allocation, we model the coded edge federation based on evolutionary game theory. Since the replicator dynamics of the classical evolutionary game are unable to model economic-aware EIPs which memorize past decisions and utilities, we propose fractional replicator dynamics with a power-law fading memory via Caputo fractional derivatives. The proposed dynamics allow us to study a broad spectrum of EIP dynamic behaviors, such as EIP sensitivity and aggressiveness in strategy adaptation, which classical replicator dynamics cannot capture. Theoretical analysis and extensive numerical results justify the existence, uniqueness, and stability of the equilibrium in the fractional evolutionary game. The influence of the content and the length of the memory on the rate of convergence is also investigated.
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