## Section: New Results

### Generalized Nash Equilibria for Platform-as-a-Service Clouds

Participants : Jonatha Anselmi, Danilo Ardagna, Mauro Passacantando.

Cloud computing is an emerging technology that allows to access computing resources on a pay-per-use basis. The main challenges in this area are the cient performance management and the energy costs minimization. In this work we model the service provisioning problem of Cloud Platform-as-a-Service systems as a Generalized Nash Equilibrium Problem and show that a potential function for the game exists. Moreover, we prove that the social optimum problem is convex and we derive some properties of social optima from the corresponding Karush-Kuhn-Tucker system. Next, we propose a distributed solution algorithm based on the best response dynamics and we prove its convergence to generalized Nash equilibria. Finally, we numerically evaluate equilibria in terms of their efficiency with respect to the social optimum of the Cloud by varying our algorithm initial solution. Numerical results show that our algorithm is scalable and very efficient and thus can be adopted for the run-time management of very large scale systems. This work has been published in an international journal; see [12] .