Studying dynamic equilibrium of cloud computing adoption with application of Mean Field Games

Computing is undergoing a substantial shift from client/server to the cloud. The enthusiasm for cloud infrastructures is not only present in the business world, but also extends to government agencies. Managers of both segments thus need to have a clear view of how this new era will evolve in the coming years, in order to appropriately react to a changing economic and technological environment. In this study, we explore the dynamic equilibrium of cloud computing adoption through the application of Mean Field Games. In our formulation, each agent (i.e., each firm or government agency) arbitrates between "continuing to implement the traditional on-site computing paradigm" and "moving to adopt the cloud computing paradigm". To decide on his level of moving to the cloud computing paradigm, each agent will optimize a total cost that consists of two components: the effort cost of moving to the cloud computing paradigm and the adoption cost of implementing the cloud computing paradigm. In the formulation, the adoption cost is linked to the general trend of decisions on the computing paradigm adoption. Thus, an agent's optimal level of transition to the cloud computing paradigm is not only dependent on his own effort and adoption costs but also affected by the general trend of adoption decisions. The problem is solved by a system of partial differential equations (PDEs), that is, mean field games PDEs, which consists of a backward PDE, the Hamilton Jacobi Bellman equation for a controlled problem, and a forward Fokker-Planck equation transported by the optimal control from the backward HJB equation. Thus, the solution to the forward Fokker-Planck equation enables us to study the dynamic evolution of the density of the cloud computing adoption. It therefore allows us to investigate the impact of the general trend of technology adoption decisions on a firm's optimal decision of technology transition.